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受欢迎的代数 >

(x+5)^2+(x-8)^2=25

解答

(x + 5)^{2} + (x - 8)^{2} = 25

解答

x = \frac{3}{2} + i \frac{119}{2}, x = \frac{3}{2} - i \frac{119}{2}

求解步骤

(x + 5)^{2} + (x - 8)^{2} = 25

展开

(x + 5)^{2} + (x - 8)^{2} : 2 x^{2} - 6 x + 89

2 x^{2} - 6 x + 89 = 25

将

25

para o lado esquerdo

2 x^{2} - 6 x + 64 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 \cdot 64}{2 \cdot 2}

化简

(- 6)^{2} - 4 \cdot 2 \cdot 64 : 2119 i

x_{1, 2} = \frac{- ( - 6 ) \pm 2 119 i}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( - 6 ) + 2 119 i}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 119 i}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 119 i}{2 \cdot 2} : \frac{3}{2} + i \frac{119}{2}

x = \frac{- ( - 6 ) - 2 119 i}{2 \cdot 2} : \frac{3}{2} - i \frac{119}{2}

二次方程组的解是:

x = \frac{3}{2} + i \frac{119}{2}, x = \frac{3}{2} - i \frac{119}{2}

作图

流行的例子

(x-3)^2-(2x+5)^2=-26x-28

(x - 3)^{2} - (2 x + 5)^{2} = - 26 x - 28

c^{2} - 9 c + 11 = 0

3x^2-6=(x+2)(x-3)

3 x^{2} - 6 = (x + 2) (x - 3)

8f^2+11f=2f^2+3(2f-5)+21

8 f^{2} + 11 f = 2 f^{2} + 3 (2 f - 5) + 21

solvefor y,3y-2xy-3y^2=0

so l v e f or y, 3 y - 2 x y - 3 y^{2} = 0