Question

a^2+1/a^2+2 factorise​

Answer 1

$Given \: a^{2} + \frac{1}{a^{2}} + 2$

$= a^{2} + \frac{1}{a^{2}} + 2\times a \times \frac{1}{a}$

$= \Big( a + \frac{1}{a}\Big)^{2}$

/* By algebraic identity */

$\boxed{\pink{ x^{2} + 2 \times x \times y + y^{2} = ( x + y )^{2} }}$

$= \Big( a + \frac{1}{a}\Big)\Big( a + \frac{1}{a}\Big)$

Therefore.,

$\red{ Factors \: of \: a^{2} + \frac{1}{a^{2}} + 2}$

$= \Big( a + \frac{1}{a}\Big)\Big( a + \frac{1}{a}\Big)$

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