What-is-maximum-value-x-3-y-3-3xy-when-x-y-8-

Question Number 118701 by bemath last updated on 19/Oct/20

W h a t i s m a x i m u m v a l u e

x^{3} y^{3} + 3 x y w h e n x + y = 8 ?

Commented by PRITHWISH SEN 2 last updated on 19/Oct/20

4144

Commented by bemath last updated on 19/Oct/20

x = y = 4

{(16)}^{3} + 3 \times 4 \times 4 = 4144

Answered by mr W last updated on 19/Oct/20

{(x y)}^{3} + 3 (x y)

= {(\sqrt{x y})}^{6} + 3 {(\sqrt{x y})}^{2}

⩽ {(\frac{x + y}{2})}^{6} + 3 {(\frac{x + y}{2})}^{2} = 4^{6} + 3 \times 4^{2} = 4144

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