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Question Number 142325 by loveineq last updated on 30/May/21

$$\mathrm{Given}\mathrm{that}a⩾1⩾b>0.\mathrm{Prove}\mathrm{the}\mathrm{followings}:$$ $$\left(1\right)\frac{1}{2}{(a-b)}^2⩽{(a-1)}^2+{(1-b)}^2⩽{(a-b)}^2$$ $$\left(2\right)\frac{1}{4}{(a-b)}^3⩽{(a-1)}^3+{(1-b)}^3⩽{(a-b)}^3$$ $$$$

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