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受欢迎的代数 >

solvefor x,((p-3)(p+5))*x^2-4x+8=0

解答

求解

x, ((p - 3) (p + 5)) \cdot x^{2} - 4 x + 8 = 0

解答

x = \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}, x = \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}; p \neq = 3, p \neq = - 5

求解步骤

((p - 3) (p + 5)) x^{2} - 4 x + 8 = 0

展开

((p - 3) (p + 5)) x^{2} - 4 x + 8 : x^{2} p^{2} + 2 x^{2} p - 15 x^{2} - 4 x + 8

x^{2} p^{2} + 2 x^{2} p - 15 x^{2} - 4 x + 8 = 0

改写成标准形式

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

(p^{2} + 2 p - 15) x^{2} - 4 x + 8 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 ( p ^{2} + 2 p - 15 ) \cdot 8}{2 ( p ^{2} + 2 p - 15 )}

化简

(- 4)^{2} - 4 (p^{2} + 2 p - 15) \cdot 8 : 4 - 2 p^{2} - 4 p + 31

x_{1, 2} = \frac{- ( - 4 ) \pm 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}; p \neq = 3, p \neq = - 5

将解分隔开

x_{1} = \frac{- ( - 4 ) + 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}, x_{2} = \frac{- ( - 4 ) - 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )}

x = \frac{- ( - 4 ) + 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )} : \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}

x = \frac{- ( - 4 ) - 4 - 2 p ^{2} - 4 p + 31}{2 ( p ^{2} + 2 p - 15 )} : \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}

二次方程组的解是:

x = \frac{2 ( - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}, x = \frac{2 ( - - 2 p ^{2} - 4 p + 31 + 1 )}{p ^{2} + 2 p - 15}; p \neq = 3, p \neq = - 5

作图

流行的例子

xlog_{10}(10)(x-3)=2

x lo g_{10} (10) (x - 3) = 2

solvefor x,2x^2-4xy+2y^2-5x-5=0

so l v e f or x, 2 x^{2} - 4 x y + 2 y^{2} - 5 x - 5 = 0

solvefor x,z^2= 324/972 (x^2+y^2)

so l v e f or x, z^{2} = \frac{324}{972} (x^{2} + y^{2})

solvefor x,x^2-3x-m(m+3)=0

so l v e f or x, x^{2} - 3 x - m (m + 3) = 0

solvefor x,3x^2y+2y=5x

so l v e f or x, 3 x^{2} y + 2 y = 5 x