MHB Confused: Seeking Help on Problem Solution

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I am not entirely sure if I solved this problem correctly. Please let me know if my reasoning is flawed. Thank you and I appreciate your help greatly.
 

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Albert Einstein said:
I am not entirely sure if I solved this problem correctly. Please let me know if my reasoning is flawed. Thank you and I appreciate your help greatly.
 

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In the first, post your "bounding" is wrong. $x^2(x^2- 2)$ is less than or equal to $-x^2$.

For the second, yes, that is correct.
 

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