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受欢迎的代数 >

(3x-4)^2-6=(2x-5)^2

解答

(3 x - 4)^{2} - 6 = (2 x - 5)^{2}

解答

x = \frac{2 + 79}{5}, x = \frac{2 - 79}{5}

+1

十进制

x = 2.17763 \dots, x = - 1.37763 \dots

求解步骤

(3 x - 4)^{2} - 6 = (2 x - 5)^{2}

展开

(3 x - 4)^{2} - 6 : 9 x^{2} - 24 x + 10

展开

(2 x - 5)^{2} : 4 x^{2} - 20 x + 25

9 x^{2} - 24 x + 10 = 4 x^{2} - 20 x + 25

将

25

para o lado esquerdo

9 x^{2} - 24 x - 15 = 4 x^{2} - 20 x

将

20 x

para o lado esquerdo

9 x^{2} - 4 x - 15 = 4 x^{2}

将

4 x^{2}

para o lado esquerdo

5 x^{2} - 4 x - 15 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 5 ( - 15 )}{2 \cdot 5}

(- 4)^{2} - 4 \cdot 5 (- 15) = 279

x_{1, 2} = \frac{- ( - 4 ) \pm 2 79}{2 \cdot 5}

将解分隔开

x_{1} = \frac{- ( - 4 ) + 2 79}{2 \cdot 5}, x_{2} = \frac{- ( - 4 ) - 2 79}{2 \cdot 5}

x = \frac{- ( - 4 ) + 2 79}{2 \cdot 5} : \frac{2 + 79}{5}

x = \frac{- ( - 4 ) - 2 79}{2 \cdot 5} : \frac{2 - 79}{5}

二次方程组的解是:

x = \frac{2 + 79}{5}, x = \frac{2 - 79}{5}

作图

流行的例子

solvefor x,6xy-3x^2=0

so l v e f or x, 6 x y - 3 x^{2} = 0

completesquare 15+6x-9x^2

co m pl e t es q u a re 15 + 6 x - 9 x^{2}

x^{2} + 9 = 5

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2 y^{2} + 8 y - 10 = 0