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受欢迎的代数 >

4(x+3)^2=25(x-2)^2

解答

4 (x + 3)^{2} = 25 (x - 2)^{2}

解答

x = \frac{4}{7}, x = \frac{16}{3}

+1

十进制

x = 0.57142 \dots, x = 5.33333 \dots

求解步骤

4 (x + 3)^{2} = 25 (x - 2)^{2}

展开

4 (x + 3)^{2} : 4 x^{2} + 24 x + 36

展开

25 (x - 2)^{2} : 25 x^{2} - 100 x + 100

4 x^{2} + 24 x + 36 = 25 x^{2} - 100 x + 100

将

100

para o lado esquerdo

4 x^{2} + 24 x - 64 = 25 x^{2} - 100 x

将

100 x

para o lado esquerdo

4 x^{2} + 124 x - 64 = 25 x^{2}

将

25 x^{2}

para o lado esquerdo

- 21 x^{2} + 124 x - 64 = 0

使用求根公式求解

x_{1, 2} = \frac{- 124 \pm 12 4 ^{2} - 4 ( - 21 ) ( - 64 )}{2 ( - 21 )}

12 4^{2} - 4 (- 21) (- 64) = 100

x_{1, 2} = \frac{- 124 \pm 100}{2 ( - 21 )}

将解分隔开

x_{1} = \frac{- 124 + 100}{2 ( - 21 )}, x_{2} = \frac{- 124 - 100}{2 ( - 21 )}

x = \frac{- 124 + 100}{2 ( - 21 )} : \frac{4}{7}

x = \frac{- 124 - 100}{2 ( - 21 )} : \frac{16}{3}

二次方程组的解是:

x = \frac{4}{7}, x = \frac{16}{3}

作图

流行的例子

solvefor x,x^2-6xy+y^2=0

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

solvefor x,2px^2+3x-2-5p=0

so l v e f or x, 2 p x^{2} + 3 x - 2 - 5 p = 0

25(x+1)= 7/2 x^2

25 (x + 1) = \frac{7}{2} x^{2}

1 x^{2} + x + 1 = 0

(y - 4) (y - 9) = 0