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受欢迎的代数 >

solvefor x,hx^2+9h^2x=3+x

解答

求解

x, h x^{2} + 9 h^{2} x = 3 + x

解答

x = \frac{- 9 h ^{2} + 1 + ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}, x = \frac{- 9 h ^{2} + 1 - ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}; h \neq = 0

求解步骤

h x^{2} + 9 h^{2} x = 3 + x

将

x

para o lado esquerdo

h x^{2} + 9 h^{2} x - x = 3

将

3

para o lado esquerdo

h x^{2} + 9 h^{2} x - x - 3 = 0

改写成标准形式

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

h x^{2} + (9 h^{2} - 1) x - 3 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 9 h ^{2} - 1 ) \pm ( 9 h ^{2} - 1 ) ^{2} - 4 h ( - 3 )}{2 h}

化简

(9 h^{2} - 1)^{2} - 4 h (- 3) : (9 h^{2} - 1)^{2} + 12 h

x_{1, 2} = \frac{- ( 9 h ^{2} - 1 ) \pm ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}; h \neq = 0

将解分隔开

x_{1} = \frac{- ( 9 h ^{2} - 1 ) + ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}, x_{2} = \frac{- ( 9 h ^{2} - 1 ) - ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}

x = \frac{- ( 9 h ^{2} - 1 ) + ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h} : \frac{- 9 h ^{2} + 1 + ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}

x = \frac{- ( 9 h ^{2} - 1 ) - ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h} : \frac{- 9 h ^{2} + 1 - ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}

二次方程组的解是:

x = \frac{- 9 h ^{2} + 1 + ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}, x = \frac{- 9 h ^{2} + 1 - ( 9 h ^{2} - 1 ) ^{2} + 12 h}{2 h}; h \neq = 0

作图

流行的例子

3 x^{2} - 64 = 0

h^{2} + 3 h = 30

2 (x - 6)^{2} + 10 = 20

5 = x^{2} - 4 x

4 p^{2} + 19 p + 12 = - 5