if-x-2-y-2-z-2-1-maximum-value-xy-2yz-

Question Number 218005 by jacklau last updated on 25/Mar/25

if x^{2} + y^{2} + z^{2} = 1,

maximum value x y + 2 yz = \dots

Commented by Ghisom last updated on 26/Mar/25

I get

- \frac{\sqrt{5}}{2} ⩽ (x + 2 z) y ⩽ \frac{\sqrt{5}}{2}

Commented by mr W last updated on 26/Mar/25

y e s . t h i s i s c o r r e c t . m a x i m u m i s a t

x = \frac{1}{\sqrt{10}}, y = \frac{1}{\sqrt{2}}, z = \frac{2}{\sqrt{10}}

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