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受欢迎的代数 >

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

解答

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

解答

x = \frac{9 + 5}{2}, x = \frac{9 - 5}{2}

+1

十进制

x = 5.61803 \dots, x = 3.38196 \dots

求解步骤

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

展开

(x + 3) (x - 3) - (x - 2)^{2} : 4 x - 13

展开

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

4 x - 13 = 6 + x^{2} - 5 x

交换两边

6 + x^{2} - 5 x = 4 x - 13

将

13

para o lado esquerdo

x^{2} - 5 x + 19 = 4 x

将

4 x

para o lado esquerdo

x^{2} - 9 x + 19 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 1 \cdot 19}{2 \cdot 1}

(- 9)^{2} - 4 \cdot 1 \cdot 19 = 5

x_{1, 2} = \frac{- ( - 9 ) \pm 5}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( - 9 ) + 5}{2 \cdot 1}, x_{2} = \frac{- ( - 9 ) - 5}{2 \cdot 1}

x = \frac{- ( - 9 ) + 5}{2 \cdot 1} : \frac{9 + 5}{2}

x = \frac{- ( - 9 ) - 5}{2 \cdot 1} : \frac{9 - 5}{2}

二次方程组的解是:

x = \frac{9 + 5}{2}, x = \frac{9 - 5}{2}

作图

流行的例子

-3l^2+20l+100=0

- 3 l^{2} + 20 l + 100 = 0

3(x^2-2x)=8(x-2)+8

3 (x^{2} - 2 x) = 8 (x - 2) + 8

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

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

0.5^2+0.5^2=x^2

0. 5^{2} + 0. 5^{2} = x^{2}

solvefor x,P_{2}(x)=1-1/2 x^2

so l v e f or x, P_{2} (x) = 1 - \frac{1}{2} x^{2}