Factorize: a^{2}+frac{1}{a^{2}}+3-2 a-frac{2} | vedclass

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(D) Given expression: $a^{2}+\frac{1}{a^{2}}+3-2 a-\frac{2}{a}$Rearrange the terms to form a perfect square:$= (a^{2}+\frac{1}{a^{2}}+2) - 2a - \frac{

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$\left(a+\frac{1}{a}-1\right)\left(a+\frac{1}{a}-1\right)$

Vedclass · Answer

(D) Given expression: $a^{2}+\frac{1}{a^{2}}+3-2 a-\frac{2}{a}$Rearrange the terms to form a perfect square:$= (a^{2}+\frac{1}{a^{2}}+2) - 2a - \frac{2}{a} + 1$$= (a+\frac{1}{a})^{2} - 2(a+\frac{1}{a}) + 1$Let $x = a+\frac{1}{a}$. Then the expression becomes:$= x^{2} - 2x + 1$This is a perfect square of the form $(x-1)^{2}$:$= (x-1)^{2}$Substituting back $x = a+\frac{1}{a}$:$= (a+\frac{1}{a}-1)^{2}$$= (a+\frac{1}{a}-1)(a+\frac{1}{a}-1)$

Factorize: $a^{2}+\frac{1}{a^{2}}+3-2 a-\frac{2}{a}$

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