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受欢迎的 Geometry >

solvefor x,(x-2)^2+(x-3)^2=r(x)^2

解答

求解

x, (x - 2)^{2} + (x - 3)^{2} = r (x)^{2}

解答

x = \frac{5 + 13 r - 1}{2 - r}, x = \frac{5 - 13 r - 1}{2 - r}; r \neq = 2

求解步骤

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

展开

(x - 2)^{2} + (x - 3)^{2} : 2 x^{2} - 10 x + 13

2 x^{2} - 10 x + 13 = r x^{2}

将

r x^{2}

para o lado esquerdo

2 x^{2} - 10 x + 13 - r x^{2} = 0

改写成标准形式

a x^{2} + b x + c = 0

(2 - r) x^{2} - 10 x + 13 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 ( 2 - r ) \cdot 13}{2 ( 2 - r )}

化简

(- 10)^{2} - 4 (2 - r) \cdot 13 : 2 13 r - 1

x_{1, 2} = \frac{- ( - 10 ) \pm 2 13 r - 1}{2 ( 2 - r )}; r \neq = 2

将解分隔开

x_{1} = \frac{- ( - 10 ) + 2 13 r - 1}{2 ( 2 - r )}, x_{2} = \frac{- ( - 10 ) - 2 13 r - 1}{2 ( 2 - r )}

x = \frac{- ( - 10 ) + 2 13 r - 1}{2 ( 2 - r )} : \frac{5 + 13 r - 1}{2 - r}

x = \frac{- ( - 10 ) - 2 13 r - 1}{2 ( 2 - r )} : \frac{5 - 13 r - 1}{2 - r}

二次方程组的解是:

x = \frac{5 + 13 r - 1}{2 - r}, x = \frac{5 - 13 r - 1}{2 - r}; r \neq = 2

作图

流行的例子

x^{2} - y^{2} + 2 = 0

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

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

-4x^2+7y^2+8x+42y+31=0

- 4 x^{2} + 7 y^{2} + 8 x + 42 y + 31 = 0

4x^2-4y^2-4x+8y-19=0

4 x^{2} - 4 y^{2} - 4 x + 8 y - 19 = 0