Question

please answer this question

Answer 1

m^2 - n^2 =

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

or

$\frac{ {a}^{4} - 1}{ {a}^{2} }$

Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• $\sf a \: + \: \dfrac{1}{a} \: = \: m \: , \: a \: - \: \dfrac{1}{a} \: = \: n$

• a ≠ 0

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• m² - n²

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• m² - n²

Here,

• $\sf a \: + \: \dfrac{1}{a} \: = \: m$

• $\sf a \: - \: \dfrac{1}{a} \: = \: n$

We know that,

• a² - b² = (a + b)(a - b)

Here,

• m² - n² = (m + n)(m - n)

Substituting the values,

• (m + n)(m - n)

• $\sf \bigg(a \: + \: \dfrac{1}{a} \: + \: a \: - \: \dfrac{1}{a}\bigg)\bigg(a \: + \: \dfrac{1}{a} \: - \big(a \: - \: \dfrac{1}{a}\big)\bigg)$

• $\sf \bigg(a \: + \: \dfrac{1}{a} \: + \: a \: - \: \dfrac{1}{a}\bigg)\bigg(a \: + \: \dfrac{1}{a} \: - a \: + \: \dfrac{1}{a}\bigg)$

• $\sf \bigg(a \: \cancel{+ \: \dfrac{1}{a}} \: + \: a \: \cancel{- \: \dfrac{1}{a}}\bigg)\bigg(\cancel{a} \: + \: \dfrac{1}{a} \: \cancel{- \: a} \: + \: \dfrac{1}{a}\bigg)$

• $\sf \big(a \: + \: a \big)\bigg(\dfrac{1}{a} \: + \: \dfrac{1}{a}\bigg)$

• $\sf \big(2a \big)\bigg(\dfrac{2}{a} \bigg)$

• $\sf 2a \: * \: \dfrac{2}{a}$

• $\sf 2\cancel{a} \: * \: \dfrac{2}{\cancel{a}}$

• $\sf 2 \: * \: \dfrac{2}{1}$

• $\sf 2 \: * \: 2$

• $\sf 4$

Therefore,

• m² - n² = 4