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Question Number 162946 by HongKing last updated on 02/Jan/22

	Answered by ajfour last updated on 02/Jan/22

	${(x^{2} + y^{2} + z^{2})}^{2} = x^{2} + y^{2} + z^{2} + 2 (x^{2} y^{2} +$ $y^{2} z^{2} + z^{2} x^{2})$ $s a y s^{2} = s + 2 k$ $\frac{\partial P}{\partial x} = 0 \Rightarrow \frac{z^{2}}{x^{2}} = \frac{2 x}{y}$ $\frac{\partial P}{\partial y} = 0 \Rightarrow \frac{x^{2}}{y^{2}} = \frac{2 y}{z}$ $\frac{\partial P}{\partial z} = 0 \Rightarrow \frac{y^{2}}{z^{2}} = \frac{2 z}{x}$ $\Rightarrow x = y = z = 1$ $P_{m i n} = 3 .$
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