Question

the square root of x⁴+1/x⁴-2 is ...... details please​

Answer 1

Answer:

The answer is -

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

Step-by-step explanation:

To find the square root of $x^{4}$ + $\frac{1}{x^{4}} - 2$

Follow the identity

As we know that $(a - b)^{2}$  = $a^{2}$ + 2ab + $b^{2}$

So,

${x^{4} + \frac{1}{x^{4}}-2}$ =  $(x^{2})^{2}$ - 2($x^{2}$)($\frac{1}{x^{2}}$) + $(\frac{1}{x^{2}})^{2}$ [Using identity $(a + b)^{2}$  = $a^{2}$ + 2ab + $b^{2}$]

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

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