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受欢迎的代数 >

x[x-3(12-3x)+2x]=5(2x^2-1)

解答

x [x - 3 (12 - 3 x) + 2 x] = 5 (2 x^{2} - 1)

解答

x = \frac{18 + 314}{2}, x = \frac{18 - 314}{2}

+1

十进制

x = 17.86002 \dots, x = 0.13997 \dots

求解步骤

x [x - 3 (12 - 3 x) + 2 x] = 5 (2 x^{2} - 1)

展开

x (x - 3 (12 - 3 x) + 2 x) : 12 x^{2} - 36 x

展开

5 (2 x^{2} - 1) : 10 x^{2} - 5

12 x^{2} - 36 x = 10 x^{2} - 5

将

5

para o lado esquerdo

12 x^{2} - 36 x + 5 = 10 x^{2}

将

10 x^{2}

para o lado esquerdo

2 x^{2} - 36 x + 5 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 36 ) \pm ( - 36 ) ^{2} - 4 \cdot 2 \cdot 5}{2 \cdot 2}

(- 36)^{2} - 4 \cdot 2 \cdot 5 = 2314

x_{1, 2} = \frac{- ( - 36 ) \pm 2 314}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( - 36 ) + 2 314}{2 \cdot 2}, x_{2} = \frac{- ( - 36 ) - 2 314}{2 \cdot 2}

x = \frac{- ( - 36 ) + 2 314}{2 \cdot 2} : \frac{18 + 314}{2}

x = \frac{- ( - 36 ) - 2 314}{2 \cdot 2} : \frac{18 - 314}{2}

二次方程组的解是:

x = \frac{18 + 314}{2}, x = \frac{18 - 314}{2}

作图

流行的例子

10 x - 15 x^{2} = 0

solvefor t,f=(a-bt)^2

so l v e f or t, f = (a - b t)^{2}

2 u^{2} - 3 u - 2 = 0

x^{2} + (- 5) x + 6 = 0

solvefor x,x^2+y^2=1-3/2 xy

so l v e f or x, x^{2} + y^{2} = 1 - \frac{3}{2} x y