EIs \(x^4 + y^4 > z^4\)

(1) \(x^2 + y^2 > z^2\)

(2) \(x + y > z\)

It is obviously that x=10000, y=10000, z=1 satisfies both conditions and answer is "true".

So, I will try to construct example that satisfies both condition but answer is "false"

1. let x=y and z=1 for simplicity.

2. we need x<1 because \(x^n\) will decrease when the power increases.

consider the fist condition: \(2*x^2>1\) --> \(x>\sqrt{0.5} \approx 0.7\)

3. try x=0.8 (it satisfies both conditions): \(2*0.8^4 = 2*0.64^2 < 2*0.7^2 < 2*0.49 < 1\) bingo!

Here, I've tried to clarify my logic (for myself also

) when I construct examples.....just exercise

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