Question

Factorize: a2 + 1/a2 +2​

Answer 1

Answer:

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

Given:

$(a^{2} + \frac{1}{a^{2} }+2)$​

To Find:

Factorization

Step-by-step explanation:

It is given that,

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

Rearrange the terms:

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

middle term can be written as

$2 = (a)(\frac{1}{a})$

So,  

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

Now, $(a^{2} + 2ab + b^{2}) = (a +b)^{2}$

Therefore,

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

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

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

#SPJ2

Answer 2

Answer : (a+b)^2

hope y'all understand