What is sqrt(1+1/4 (x^6+2x^3+1/(x^6))) ?

The solution to sqrt(1+1/4 (x^6+2x^3+1/(x^6))) is (sqrt(4x^6+x^{12)+2x^9+1})/(2x^3)

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simplify sqrt(1+1/4 (x^6+2x^3+1/(x^6)))

simplify

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}}

Solution steps

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

Simplify

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}}

Apply radical rule:

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

assuming

a \geq 0, b \geq 0

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

Simplify

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

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

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

\frac{2 10 ( e ^{9} - 1 )}{3}

(- 8 + 12) (- 8 - 0) (- 8 - 8) (- 8 - 12)

\frac{7 x - 1}{( x + 2 ) ( x - 1 )}

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

What is sqrt(1+1/4 (x^6+2x^3+1/(x^6))) ?
The solution to sqrt(1+1/4 (x^6+2x^3+1/(x^6))) is (sqrt(4x^6+x^{12)+2x^9+1})/(2x^3)