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受欢迎的代数 >

solvefor x,f=2x^2+xy+y^2+100-z(x+y-100)

解答

求解

x, f = 2 x^{2} + x y + y^{2} + 100 - z (x + y - 100)

解答

x = \frac{- y + z + - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}, x = \frac{- y + z - - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}

求解步骤

f = 2 x^{2} + x y + y^{2} + 100 - z (x + y - 100)

展开

2 x^{2} + x y + y^{2} + 100 - z (x + y - 100) : 2 x^{2} + x y + y^{2} + 100 - x z - yz + 100 z

f = 2 x^{2} + x y + y^{2} + 100 - x z - yz + 100 z

交换两边

2 x^{2} + x y + y^{2} + 100 - x z - yz + 100 z = f

将

f

para o lado esquerdo

2 x^{2} + x y + y^{2} + 100 - x z - yz + 100 z - f = 0

改写成标准形式

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

2 x^{2} + (y - z) x + y^{2} + 100 - yz + 100 z - f = 0

使用求根公式求解

x_{1, 2} = \frac{- ( y - z ) \pm ( y - z ) ^{2} - 4 \cdot 2 ( y ^{2} + 100 - yz + 100 z - f )}{2 \cdot 2}

化简

(y - z)^{2} - 4 \cdot 2 (y^{2} + 100 - yz + 100 z - f) : - 7 y^{2} + 6 yz + z^{2} - 800 z + 8 f - 800

x_{1, 2} = \frac{- ( y - z ) \pm - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( y - z ) + - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{2 \cdot 2}, x_{2} = \frac{- ( y - z ) - - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{2 \cdot 2}

x = \frac{- ( y - z ) + - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{2 \cdot 2} : \frac{- y + z + - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}

x = \frac{- ( y - z ) - - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{2 \cdot 2} : \frac{- y + z - - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}

二次方程组的解是:

x = \frac{- y + z + - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}, x = \frac{- y + z - - 7 y ^{2} + 6 yz + z ^{2} - 800 z + 8 f - 800}{4}

作图

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