化简 sqrt(1+1/4 (x^6+2x^3+1/(x^6)))

解答

化简

1 + \frac{1}{4} (x^{6} + 2 x^{3} + \frac{1}{x ^{6}})

\frac{4 x ^{6} + x ^{12} + 2 x ^{9} + 1}{2 x ^{3}}

求解步骤

1 + \frac{1}{4} (x^{6} + 2 x^{3} + \frac{1}{x ^{6}})

化简

1 + \frac{1}{4} (x^{6} + 2 x^{3} + \frac{1}{x ^{6}}) : \frac{4 x ^{6} + x ^{12} + 2 x ^{9} + 1}{4 x ^{6}}

= \frac{4 x ^{6} + x ^{12} + 2 x ^{9} + 1}{4 x ^{6}}

使用根式运算法则:

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

假定

a \geq 0, b \geq 0

= \frac{4 x ^{6} + x ^{12} + 2 x ^{9} + 1}{4 x ^{6}}

化简

4 x^{6} : 2 x^{3}

= \frac{4 x ^{6} + x ^{12} + 2 x ^{9} + 1}{2 x ^{3}}

e x p an d (y^{4} + 2 - x) d x

e x p an d \frac{2 10 ( e ^{9} - 1 )}{3}

e x p an d (- 8 + 12) (- 8 - 0) (- 8 - 8) (- 8 - 12)

e x p an d \frac{7 x - 1}{( x + 2 ) ( x - 1 )}

\frac{d}{d x} ((z) (ln (x^{2} + z^{2}) + y z^{3} + 2 x^{2}))