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Algebraic Solutions [closed]
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Any elegant solutions?
1.) If $(a,b)$ is the solution of the system $sqrtx+y + sqrtx-y =4$, $x^2 −y^2 =9$, then $displaystyle fracaba + b$ has a value of?
My answer is $20/9$
algebra-precalculus systems-of-equations radicals substitution
edited Aug 1 at 10:36
Javi
2,1481625
asked Aug 1 at 9:52
TCSHS
124
closed as off-topic by Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma Aug 1 at 18:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma
add a comment |Â
up vote
-2
down vote
favorite
Any elegant solutions?
1.) If $(a,b)$ is the solution of the system $sqrtx+y + sqrtx-y =4$, $x^2 −y^2 =9$, then $displaystyle fracaba + b$ has a value of?
My answer is $20/9$
algebra-precalculus systems-of-equations radicals substitution
edited Aug 1 at 10:36
Javi
2,1481625
asked Aug 1 at 9:52
TCSHS
124
closed as off-topic by Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma Aug 1 at 18:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma
1
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Any elegant solutions?
1.) If $(a,b)$ is the solution of the system $sqrtx+y + sqrtx-y =4$, $x^2 −y^2 =9$, then $displaystyle fracaba + b$ has a value of?
My answer is $20/9$
algebra-precalculus systems-of-equations radicals substitution
edited Aug 1 at 10:36
Javi
2,1481625
asked Aug 1 at 9:52
TCSHS
124
Any elegant solutions?
1.) If $(a,b)$ is the solution of the system $sqrtx+y + sqrtx-y =4$, $x^2 −y^2 =9$, then $displaystyle fracaba + b$ has a value of?
My answer is $20/9$
algebra-precalculus systems-of-equations radicals substitution
edited Aug 1 at 10:36
Javi
2,1481625
asked Aug 1 at 9:52
TCSHS
124
edited Aug 1 at 10:36
Javi
2,1481625
edited Aug 1 at 10:36
Javi
2,1481625
edited Aug 1 at 10:36
Javi
2,1481625
2,1481625
asked Aug 1 at 9:52
TCSHS
124
asked Aug 1 at 9:52
TCSHS
124
asked Aug 1 at 9:52
TCSHS
124
124
closed as off-topic by Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma Aug 1 at 18:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma
closed as off-topic by Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma Aug 1 at 18:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Arnaud Mortier, Simply Beautiful Art, Isaac Browne, Mostafa Ayaz, John Ma
1
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33
add a comment |Â
1
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33
1
1
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
0
down vote
Let $sqrtx+y=p$ and $sqrtx-y=q$.
Thus, $pgeq0$, $qgeq0$,
$$p+q=4$$ and $$p^2q^2=9.$$
Can you end it now?
I got $frac209$ or $-20.$
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
add a comment |Â
up vote
0
down vote
Your answer is wrong. Let $$m=sqrtx+y\n=sqrtx-y$$therefore$$m+n=4\m^2n^2=9$$by direct investigation we obtain$$m=1\n=3$$or $$a=5\b=-4$$therefore$$dfracaba+b=dfrac-4times 5-4+5=-20$$
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Let $sqrtx+y=p$ and $sqrtx-y=q$.
Thus, $pgeq0$, $qgeq0$,
$$p+q=4$$ and $$p^2q^2=9.$$
Can you end it now?
I got $frac209$ or $-20.$
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
add a comment |Â
up vote
0
down vote
Let $sqrtx+y=p$ and $sqrtx-y=q$.
Thus, $pgeq0$, $qgeq0$,
$$p+q=4$$ and $$p^2q^2=9.$$
Can you end it now?
I got $frac209$ or $-20.$
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Let $sqrtx+y=p$ and $sqrtx-y=q$.
Thus, $pgeq0$, $qgeq0$,
$$p+q=4$$ and $$p^2q^2=9.$$
Can you end it now?
I got $frac209$ or $-20.$
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
Let $sqrtx+y=p$ and $sqrtx-y=q$.
Thus, $pgeq0$, $qgeq0$,
$$p+q=4$$ and $$p^2q^2=9.$$
Can you end it now?
I got $frac209$ or $-20.$
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
answered Aug 1 at 9:55
Michael Rozenberg
87.4k1577179
87.4k1577179
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
add a comment |Â
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
Is that the fastest solution you can think of, or maybe you have something faster?
– TCSHS
Aug 1 at 10:12
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
I think it's an easiest way.
– Michael Rozenberg
Aug 1 at 10:13
add a comment |Â
up vote
0
down vote
Your answer is wrong. Let $$m=sqrtx+y\n=sqrtx-y$$therefore$$m+n=4\m^2n^2=9$$by direct investigation we obtain$$m=1\n=3$$or $$a=5\b=-4$$therefore$$dfracaba+b=dfrac-4times 5-4+5=-20$$
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
add a comment |Â
up vote
0
down vote
Your answer is wrong. Let $$m=sqrtx+y\n=sqrtx-y$$therefore$$m+n=4\m^2n^2=9$$by direct investigation we obtain$$m=1\n=3$$or $$a=5\b=-4$$therefore$$dfracaba+b=dfrac-4times 5-4+5=-20$$
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Your answer is wrong. Let $$m=sqrtx+y\n=sqrtx-y$$therefore$$m+n=4\m^2n^2=9$$by direct investigation we obtain$$m=1\n=3$$or $$a=5\b=-4$$therefore$$dfracaba+b=dfrac-4times 5-4+5=-20$$
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
Your answer is wrong. Let $$m=sqrtx+y\n=sqrtx-y$$therefore$$m+n=4\m^2n^2=9$$by direct investigation we obtain$$m=1\n=3$$or $$a=5\b=-4$$therefore$$dfracaba+b=dfrac-4times 5-4+5=-20$$
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
answered Aug 1 at 18:07
Mostafa Ayaz
8,5183630
8,5183630
add a comment |Â
add a comment |Â
1
Are you sure the answer is $frac29$?
– Saucy O'Path
Aug 1 at 9:54
I mean my answer is 20/9 and not 02/9.
– TCSHS
Aug 1 at 9:56
I tried solving brutally for x and y in x^2 - y^2 = 9 and getting: x=5, y=4, or x= -5, y=4, or x=-3, y=0.
– TCSHS
Aug 1 at 9:57
But then, I want to see a better algebraic approach.
– TCSHS
Aug 1 at 10:02
Welcome to Stackexchange. You'll find that simple "Here's the statement of my exercise, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, how did you reach your answer, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Simply Beautiful Art
Aug 1 at 14:33