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Minimum value $\frac{(a^2+b^2+2c^2+3d^2)(2a^2+3b^2+6c^2+6d^2)}{(a+b)^2(c+d)^2}$

Source: 2023 Turkey TST D2 P6

March 29, 2023

minimum valueinequalities

Problem Statement

Let

a,b,c,d

be positive real numbers. What is the minimum value of

\frac{(a^2+b^2+2c^2+3d^2)(2a^2+3b^2+6c^2+6d^2)}{(a+b)^2(c+d)^2}