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受欢迎的代数 >

solvefor x,2x^2+p^2=(q-x)^2

解答

求解

x, 2 x^{2} + p^{2} = (q - x)^{2}

解答

x = - q - 2 q^{2} - p^{2}, x = - q + 2 q^{2} - p^{2}

求解步骤

2 x^{2} + p^{2} = (q - x)^{2}

展开

(q - x)^{2} : q^{2} - 2 x q + x^{2}

2 x^{2} + p^{2} = q^{2} - 2 x q + x^{2}

交换两边

q^{2} - 2 x q + x^{2} = 2 x^{2} + p^{2}

将

p^{2}

para o lado esquerdo

q^{2} - 2 x q + x^{2} - p^{2} = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

- x^{2} - 2 x q - p^{2} + q^{2} = 0

改写成标准形式

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

- x^{2} - 2 q x - p^{2} + q^{2} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 2 q ) \pm ( - 2 q ) ^{2} - 4 ( - 1 ) ( - p ^{2} + q ^{2} )}{2 ( - 1 )}

化简

(- 2 q)^{2} - 4 (- 1) (- p^{2} + q^{2}) : 2 2 q^{2} - p^{2}

x_{1, 2} = \frac{- ( - 2 q ) \pm 2 2 q ^{2} - p ^{2}}{2 ( - 1 )}

将解分隔开

x_{1} = \frac{- ( - 2 q ) + 2 2 q ^{2} - p ^{2}}{2 ( - 1 )}, x_{2} = \frac{- ( - 2 q ) - 2 2 q ^{2} - p ^{2}}{2 ( - 1 )}

x = \frac{- ( - 2 q ) + 2 2 q ^{2} - p ^{2}}{2 ( - 1 )} : - q - 2 q^{2} - p^{2}

x = \frac{- ( - 2 q ) - 2 2 q ^{2} - p ^{2}}{2 ( - 1 )} : - q + 2 q^{2} - p^{2}

二次方程组的解是:

x = - q - 2 q^{2} - p^{2}, x = - q + 2 q^{2} - p^{2}

作图

流行的例子

a \cdot x^{2} - 8 x + 4 = 0

solvefor x,x^2y^2+x^2+y^2=3736

so l v e f or x, x^{2} y^{2} + x^{2} + y^{2} = 3736

x^{2} = 4 \frac{x}{5} + \frac{1}{5}

(m-1)*x^2-2(m-1)x+1=0

(m - 1) \cdot x^{2} - 2 (m - 1) x + 1 = 0

solvefor x,y^2=((9x^2))/(36)

so l v e f or x, y^{2} = \frac{( 9 x ^{2} )}{36}