展开 sqrt((x-2)^2+(x-1/2)^2)

解答

展开

(x - 2)^{2} + (x - \frac{1}{2})^{2}

\frac{8 x ^{2} - 20 x + 17}{2}

求解步骤

(x - 2)^{2} + (x - \frac{1}{2})^{2}

乘开

(x - 2)^{2} + (x - \frac{1}{2})^{2} : 2 x^{2} - 5 x + \frac{17}{4}

= 2 x^{2} - 5 x + \frac{17}{4}

化简

2 x^{2} - 5 x + \frac{17}{4} : \frac{8 x ^{2} - 20 x + 17}{4}

= \frac{8 x ^{2} - 20 x + 17}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{8 x ^{2} - 20 x + 17}{4}

4 = 2

= \frac{8 x ^{2} - 20 x + 17}{2}

e x p an d \frac{( ( - 1 ) ^{n} - 1 )}{2}

e x p an d \frac{( x - 2 ) ( x + 1 )}{x ( x + 3 )}

e x p an d \frac{x + 1 - e ^{- x}}{e ^{- x} ( x + 1 )}

e x p an d e^{x} (1 - e^{x}) (1 + e^{x})^{10}

e x p an d 2 x e^{x} (x^{2} + e^{x})