Mixing
Verification of Proof for an Inequality Problem
Clash Royale CLAN TAG#URR8PPP
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Prove that
$$x^1116 + x^6 + dfrac1x^6+1 ge 1$$
Below is a short proof that I have attempted. Sorry if the image causes any inconvenience as it was the clearest way to display my proof (I am not able to write proper equations (such as fractions) here yet):
I don't know if my proof is convincing enough or if it is adequate. Hence, if anybody could look at it and possibly give me any suggestions on how to improve, it would be extremely appreciated.
Thanks :)
proof-verification inequality
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
asked Jul 18 at 12:00
Cameron Choi
594
add a comment |Â
up vote
2
down vote
favorite
Prove that
$$x^1116 + x^6 + dfrac1x^6+1 ge 1$$
Below is a short proof that I have attempted. Sorry if the image causes any inconvenience as it was the clearest way to display my proof (I am not able to write proper equations (such as fractions) here yet):
I don't know if my proof is convincing enough or if it is adequate. Hence, if anybody could look at it and possibly give me any suggestions on how to improve, it would be extremely appreciated.
Thanks :)
proof-verification inequality
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
asked Jul 18 at 12:00
Cameron Choi
594
As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Prove that
$$x^1116 + x^6 + dfrac1x^6+1 ge 1$$
Below is a short proof that I have attempted. Sorry if the image causes any inconvenience as it was the clearest way to display my proof (I am not able to write proper equations (such as fractions) here yet):
I don't know if my proof is convincing enough or if it is adequate. Hence, if anybody could look at it and possibly give me any suggestions on how to improve, it would be extremely appreciated.
Thanks :)
proof-verification inequality
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
asked Jul 18 at 12:00
Cameron Choi
594
Prove that
$$x^1116 + x^6 + dfrac1x^6+1 ge 1$$
Below is a short proof that I have attempted. Sorry if the image causes any inconvenience as it was the clearest way to display my proof (I am not able to write proper equations (such as fractions) here yet):
I don't know if my proof is convincing enough or if it is adequate. Hence, if anybody could look at it and possibly give me any suggestions on how to improve, it would be extremely appreciated.
Thanks :)
proof-verification inequality
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
asked Jul 18 at 12:00
Cameron Choi
594
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
edited Jul 18 at 12:02
Trần Thúc Minh TrÃ
3,62441237
3,62441237
asked Jul 18 at 12:00
Cameron Choi
594
asked Jul 18 at 12:00
Cameron Choi
594
asked Jul 18 at 12:00
Cameron Choi
594
594
As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28
add a comment |Â
As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28
As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28
add a comment |Â
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As a very first thing I notice: GREAT organization. That is far more essential to good proof writing than most people realize. At a glance, this looks convincing, and also very clean. I initially thought of just taking the derivative and finding the absolute minimum value, but that is a nightmare compared to your very simple method. Nice!
– The Count
Jul 18 at 12:07
Looks fine. Nice presentation.
– Rebellos
Jul 18 at 12:08
Let $t=x^6$, then $x^1116+x^6+frac1x^6+1=t^186+t+frac1t+1$ for $tgeq 0.$
– Riemann
Jul 18 at 12:23
Looks good. You're relying on the fact that even powers are non-negative, so perhaps that can be directly used after your simplification, rather than considering different cases.
– Macavity
Jul 18 at 12:28