Question

Factorise x^2 + 1/x^2 +2

Answer 1

QUESTION:-

✯.Factorise $\sf\therefore (x)^2 + \dfrac{1}{x^2} +2$

ANSWER✔

$\sf\therefore (x)^2 + \dfrac{1}{x^2} +2$

$\sf\implies \bigg( (x)^2 + \dfrac{1}{x^2} \bigg) +2$

$\sf\implies \bigg( \dfrac{(x^4)+1}{x^2} \bigg) + 2$

$\sf\implies \dfrac{(x^4)+1+(2x)^2}{x^2}$

$\sf\implies \dfrac{(x^4)+(2x)^2+1}{x^2}$

$\large{\boxed{\bf{ \implies \star \: \dfrac{(x^4)+(2x)^2+1}{x^2} \: \star}}}$

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Answer 2

Step-by-step explanation:

x^2 + 1/x^2 + 2

By putting the formula of ( a + b ) ^2 = a^2 + b^2 + 2ab

= ( x + 1/x )^2

= ( x )^2 + ( 1/x ) ^2 + 2 . x . 1/x

= x^2 + 1/x ^2 + 2

Hence it can be factorise as ( x + 1/x )^2 = ( x + 1/x )(x + 1/x )

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