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Let-0-a-b-lt-1-Prove-that-1-4-2-a-2-b-1-a-1-b-4-a-b-4-a-b-




Question Number 141004 by loveineq last updated on 14/May/21
Let 0 ≤ a,b < 1. Prove that                 (1/4)∙(((2−a)(2−b))/((1−a)(1−b))) ≥ ((4+a+b)/(4−a−b))
$$\mathrm{Let}\:\mathrm{0}\:\leqslant\:{a},{b}\:<\:\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}}\centerdot\frac{\left(\mathrm{2}−{a}\right)\left(\mathrm{2}−{b}\right)}{\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)}\:\geqslant\:\frac{\mathrm{4}+{a}+{b}}{\mathrm{4}−{a}−{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

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