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Given a, B, x, y ∈ positive real number, prove (a ^ 2) / x + (b ^ 2) / Y ≥ (a + b) ^ 2 / (x + y)
Inequality left and right * (a + b)
That is to say, a & sup2; + B & sup2; + (Y / x) a & sup2; + (x / y) B & sup2; ≥ (a + b) & sup2;
And (Y / x) a & sup2; + (x / y) B & sup2; ≥ 2 √ ((Y / x) a & sup2; * (x / y) B & sup2;) = 2Ab
So a & sup2; + B & sup2; + (Y / x) a & sup2; + (x / y) B & sup2; ≥ A & sup2; + B & sup2; + 2Ab = (a + b) & sup2;
So a & sup2 / x + B & sup2 / Y ≥ (a + b) & sup2; / (x + y)
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