Question

Tìm x, y, z biết :

\(x\sqrt{1-y^2}+y\sqrt{2-z^2}+z\sqrt{3-x^2}=3\)

Answer 1

\(x\sqrt{1-y^2}+y\sqrt{2-z^2}+z\sqrt{3-x^2}\le\dfrac{x^2+1-y^2}{2}+\dfrac{y^2+2-z^2}{2}+\dfrac{z^2+3-x^2}{2}=3\)

Dấu "=" xảy ra khi và chỉ khi:

\(\left\{{}\begin{matrix}x=\sqrt{1-y^2}\\y=\sqrt{2-z^2}\\z=\sqrt{3-x^2}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=1\\y=0\\z=\sqrt{2}\end{matrix}\right.\)