Question

1. The value of (a+1/a) (a-1/a) is=​

Answer 1

Answer:

You answer with step by step explanation is mentioned below:

Step-by-step explanation:

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

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

${a}^{2} - \frac{1}{ {a}^{2} }$

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Answer 2

$\sf \bigg(a\ +\ \dfrac{1}{a}\bigg)\ \times\ \bigg(a\ -\ \dfrac{1}{a}\bigg)\\\\\\According\ to\ an\ identity,\\\\\\\bigg[x\ -\ y\bigg]\ \times\ \bigg[x\ +\ y\bigg]\ =\ x^2\ -\ y^2\\\\\\Using\ this\ identity,\ let's\ assume\ x\ =\ a\ and\ y\ =\ \dfrac{1}{a}.\\\\\\\bigg[a\ -\ \dfrac{1}{a}\bigg]\ \times\ \bigg[a\ +\ \dfrac{1}{a}\bigg]\ =\ \bigg(a\bigg)^2\ -\ \bigg(\dfrac{1}{a}\bigg)^2$

$\implies\ \bf \bigg[a\ -\ \dfrac{1}{a}\bigg]\ \times\ \bigg[a\ +\ \dfrac{1}{a}\bigg]\ =\ a^2\ -\ \dfrac{1}{a^2}$

Other related identities:

$\sf (x\ +\ y)^2\ =\ x^2\ +\ 2xy\ +\ y^2\\\\\\(x\ -\ y)^2\ =\ x^2\ -\ 2xy\ +\ y^2\\\\\\x^3\ +\ y^3\ =\ (x\ +\ y)^3\ -\ 3xy(x\ +\ y)$