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Question Number 190677 by Shrinava last updated on 08/Apr/23

If x \in R

a_{1}, a_{2}, a_{3}, b_{1}, b_{2}, b_{3} > 0

Then prove that :

a_{1}^{\sin^{2} x} b_{1}^{\cos^{2} x} + a_{2}^{\sin^{2} x} b_{2}^{\cos^{2} x} + a_{3}^{\sin^{2} x} b_{3}^{\cos^{2} x} ⩽

⩽ {(a_{1} + a_{2} + a_{3})}^{\sin^{2} x} {(b_{1} + b_{2} + b_{3})}^{\cos^{2} x}