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受欢迎的代数 >

solvefor x,(x+y+2z)^2+(x+y-2z)^2=8(x+y)z

解答

求解

x, (x + y + 2 z)^{2} + (x + y - 2 z)^{2} = 8 (x + y) z

解答

x = - y + 2 z

求解步骤

(x + y + 2 z)^{2} + (x + y - 2 z)^{2} = 8 (x + y) z

展开

(x + y + 2 z)^{2} + (x + y - 2 z)^{2} : 2 y^{2} + 4 x y + 2 x^{2} + 8 z^{2}

展开

8 (x + y) z : 8 x z + 8 yz

2 y^{2} + 4 x y + 2 x^{2} + 8 z^{2} = 8 x z + 8 yz

将

8 yz

para o lado esquerdo

2 y^{2} + 4 x y + 2 x^{2} + 8 z^{2} - 8 yz = 8 x z

将

8 x z

para o lado esquerdo

2 y^{2} + 4 x y + 2 x^{2} + 8 z^{2} - 8 yz - 8 x z = 0

改写成标准形式

a x^{2} + b x + c = 0

2 x^{2} + (4 y - 8 z) x + 2 y^{2} + 8 z^{2} - 8 yz = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 4 y - 8 z ) \pm ( 4 y - 8 z ) ^{2} - 4 \cdot 2 ( 2 y ^{2} + 8 z ^{2} - 8 yz )}{2 \cdot 2}

(4 y - 8 z)^{2} - 4 \cdot 2 (2 y^{2} + 8 z^{2} - 8 yz) = 0

x_{1, 2} = \frac{- ( 4 y - 8 z ) \pm 0}{2 \cdot 2}

x = \frac{- ( 4 y - 8 z )}{2 \cdot 2}

化简

\frac{- ( 4 y - 8 z )}{2 \cdot 2} : - y + 2 z

x = - y + 2 z

二次方程组的解是:

x = - y + 2 z

作图

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