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

The solution to sqrt(1+(x^2-1/(4x^2))^2) is ((2x^2+2x+1)(2x^2-2x+1))/(4x^2)

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simplify sqrt(1+(x^2-1/(4x^2))^2)

simplify

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

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

Solution steps

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

Simplify

1 + (x^{2} - \frac{1}{4 x ^{2}})^{2} : \frac{16 x ^{8} + 8 x ^{4} + 1}{16 x ^{4}}

= \frac{16 x ^{8} + 8 x ^{4} + 1}{16 x ^{4}}

Apply radical rule:

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

assuming

a \geq 0, b \geq 0

= \frac{16 x ^{8} + 8 x ^{4} + 1}{16 x ^{4}}

Simplify

16 x^{8} + 8 x^{4} + 1 : (2 x^{2} + 2 x + 1) (2 x^{2} - 2 x + 1)

= \frac{( 2 x ^{2} + 2 x + 1 ) ( 2 x ^{2} - 2 x + 1 )}{16 x ^{4}}

Simplify

16 x^{4} : 4 x^{2}

= \frac{( 2 x ^{2} + 2 x + 1 ) ( 2 x ^{2} - 2 x + 1 )}{4 x ^{2}}

(\frac{1 + 2 i}{1 - i - i} + \frac{2 + i}{1 + 2 i}) \cdot 1 - i

2000 (1 + 0.26)^{15}

\frac{3 x - 1}{x + 2} - \frac{x - 2}{x - 1}

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

4 x^{4} - 16 x^{3} - 180 x^{2}

What is sqrt(1+(x^2-1/(4x^2))^2) ?
The solution to sqrt(1+(x^2-1/(4x^2))^2) is ((2x^2+2x+1)(2x^2-2x+1))/(4x^2)