Question

if a + 1/a = m and a - 1/a = n then find the relation b/w m and n​

Answer 1

$\huge \underline {\underline \mathtt \red{Answer }}$

${\underline{\underline \mathtt \orange {given :-}}}$

$\mathtt{\implies \frac{a + 1}{a} = m}$ ________________equation 1

$\mathtt{\implies\frac{a - 1}{a} = n}$ ________________equation 2

$\mathtt \pink {Adding \: equation \: 1 \: and \: 2}.$

$\mathtt{\implies \frac{a + 1}{ a} + \frac{a - 1}{ a} = m + n}$

$\mathtt{\implies \frac{a + 1 + a - 1}{a} = m + n}$

$\mathtt{ \implies \ \frac{2 a}{a} = m + n}$

${\blue{\fbox{\boxed {\green{\underline{ \underline \mathtt\red{\implies m + n = 2}}}}}}}$

Answer 2

a + 1/a = m

Squaring on both sides, we get

(a + 1/a)² = m²

${a}^{2} + \frac{1}{a ^{2} } + 2 = {m}^{2} \\ {a}^{2} + \frac{1}{a ^{2} } = {m}^{2} - 2 \: \: \: \: \: \: \: \: \: ....(1) \\ now \\ a - \frac{1}{a} = n \\ squaring \: on \: both \: sides \: we \: get\\ {a}^{2} + \frac{1}{a ^{2} } - 2 = {n}^{2} \\ {a}^{2} + \frac{1}{a ^{2} } = {n}^{2} + 2 \: \: \: \: \: \: \: \: \: ....(2)$

From (1) and (2) , we get

m²-2=n²+2

m²=n²+4