Given-that-a-1-b-gt-0-Prove-the-followings-1-1-2-a-b-2-a-1-2-1-b-2-a-b-2-2-1-4-a-b-3-a-1-3-1-b-3-a-b-3-

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

Given that a ⩾ 1 ⩾ b > 0 . Prove the followings :

(1) \frac{1}{2} {(a - b)}^{2} ⩽ {(a - 1)}^{2} + {(1 - b)}^{2} ⩽ {(a - b)}^{2}

(2) \frac{1}{4} {(a - b)}^{3} ⩽ {(a - 1)}^{3} + {(1 - b)}^{3} ⩽ {(a - b)}^{3}