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受欢迎的代数 >

(2x-10)^2=(x-6)^2+(x+8)^2

解答

(2 x - 10)^{2} = (x - 6)^{2} + (x + 8)^{2}

解答

x = 22, x = 0

求解步骤

(2 x - 10)^{2} = (x - 6)^{2} + (x + 8)^{2}

展开

(2 x - 10)^{2} : 4 x^{2} - 40 x + 100

展开

(x - 6)^{2} + (x + 8)^{2} : 2 x^{2} + 4 x + 100

4 x^{2} - 40 x + 100 = 2 x^{2} + 4 x + 100

将

100

para o lado esquerdo

4 x^{2} - 40 x = 2 x^{2} + 4 x

将

4 x

para o lado esquerdo

4 x^{2} - 44 x = 2 x^{2}

将

2 x^{2}

para o lado esquerdo

2 x^{2} - 44 x = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 44 ) \pm ( - 44 ) ^{2} - 4 \cdot 2 \cdot 0}{2 \cdot 2}

(- 44)^{2} - 4 \cdot 2 \cdot 0 = 44

x_{1, 2} = \frac{- ( - 44 ) \pm 44}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( - 44 ) + 44}{2 \cdot 2}, x_{2} = \frac{- ( - 44 ) - 44}{2 \cdot 2}

x = \frac{- ( - 44 ) + 44}{2 \cdot 2} : 22

x = \frac{- ( - 44 ) - 44}{2 \cdot 2} : 0

二次方程组的解是:

x = 22, x = 0

作图

流行的例子

4 x^{2} - 6 = - 12 x

3 (x^{2} - 4) = 0

x^{2} - 6 x = - 156

6 x^{2} - 72 = 0

2 x = 5 x^{2} - 3