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受欢迎的代数 >

solvefor x,(5x+4y)(5x-4y)=mx^2-ny^2

解答

求解

x, (5 x + 4 y) (5 x - 4 y) = m x^{2} - n y^{2}

解答

x = \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}, x = - \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}; m \neq = 25

求解步骤

(5 x + 4 y) (5 x - 4 y) = m x^{2} - n y^{2}

展开

(5 x + 4 y) (5 x - 4 y) : 25 x^{2} - 16 y^{2}

25 x^{2} - 16 y^{2} = m x^{2} - n y^{2}

将

n y^{2}

para o lado esquerdo

25 x^{2} - 16 y^{2} + n y^{2} = m x^{2}

将

m x^{2}

para o lado esquerdo

25 x^{2} - 16 y^{2} + n y^{2} - m x^{2} = 0

改写成标准形式

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

(25 - m) x^{2} - 16 y^{2} + n y^{2} = 0

使用求根公式求解

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 ( 25 - m ) ( - 16 y ^{2} + n y ^{2} )}{2 ( 25 - m )}

化简

0^{2} - 4 (25 - m) (- 16 y^{2} + n y^{2}) : 2 y - (- m + 25) (n - 16)

x_{1, 2} = \frac{- 0 \pm 2 y - ( - m + 25 ) ( n - 16 )}{2 ( 25 - m )}; m \neq = 25

将解分隔开

x_{1} = \frac{- 0 + 2 y - ( - m + 25 ) ( n - 16 )}{2 ( 25 - m )}, x_{2} = \frac{- 0 - 2 y - ( - m + 25 ) ( n - 16 )}{2 ( 25 - m )}

x = \frac{- 0 + 2 y - ( - m + 25 ) ( n - 16 )}{2 ( 25 - m )} : \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}

x = \frac{- 0 - 2 y - ( - m + 25 ) ( n - 16 )}{2 ( 25 - m )} : - \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}

二次方程组的解是:

x = \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}, x = - \frac{y - ( n - 16 ) ( - m + 25 )}{25 - m}; m \neq = 25

作图

流行的例子

31x^2-40x+16=6x^2

31 x^{2} - 40 x + 16 = 6 x^{2}

2 x^{2} - 7 x + 9 = x + 1

x^{2} - 4 x = - 5 x

7 w^{2} + 2 w - 3 = - w^{2}

x^{2} - 33 = 3