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Toán Lớp 9: tim x,y,z thoa man dieu kien √x + √(y-1) + √(z-2) = 1/2(x+y+z)

Home/ Toán Lớp 9: tim x,y,z thoa man dieu kien √x + √(y-1) + √(z-2) = 1/2(x+y+z)

Toán Lớp 9: tim x,y,z thoa man dieu kien √x + √(y-1) + √(z-2) = 1/2(x+y+z)

Thúy Mai Tháng Mười 23, 2022 Toán học 1 Comment 0 views

Toán Lớp 9: tim x,y,z thoa man dieu kien √x + √(y-1) + √(z-2) = 1/2(x+y+z)

Comments ( 1 )

cobexinhdep
23 Tháng Mười, 2022 at 11:44 chiều

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$\begin{array}{l} \sqrt x + \sqrt {y – 1} + \sqrt {z – 2} = \frac{1}{2}\left( {x + y + z} \right)\\ \Leftrightarrow 2\sqrt x + 2\sqrt {y – 1} + 2\sqrt {z – 2} = x + y + z\\ \Leftrightarrow x – 2\sqrt x + 1 + y – 1 – 2\sqrt {y – 1} + 1 + z – 2 + 2\sqrt {z – 2} + 1 = 0\\ \Leftrightarrow {\left( {\sqrt x – 1} \right)^2} + \left( {\sqrt {y – 1} – 1} \right) + {\left( {\sqrt {z – 2} – 1} \right)^2} = 0\\ \Leftrightarrow \left\{ \begin{array}{l} \sqrt x – 1 = 0\\ \sqrt {y – 1} – 1 = 0\\ \sqrt {z – 2} – 1 = 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = 1\\ y = 2\\ z = 3 \end{array} \right. \end{array}$

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