Question

if p-1/p =m,lets show that p²-1/p²=m²+2​

Answer 1

Step-by-step explanation:

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

${m}^{2} + 2 = {p}^{2} - \frac{1}{ {p}^{2} }$

Answer 2

$\bf\large\underline\blue{Correct\:the\: Question:-}$

• If $p-\frac{1}{p} = m$, show that $p^{2}+\frac{1}{p^{2}}=m^{2}+2$

$\bf\large\underline\blue{Solution:-}$

$p - \frac{1}{p} = m$

$\bf\small\blue{Squaring\:both\:side,\:we\:get,}$

${p}^{2} + \frac{1}{ {p}^{2} } - 2 \times \cancel{p} \times \frac{1}{ \cancel{p}} = {m}^{2}$

$\implies {p}^{2} + \frac{1}{ {p}^{2} } = {m}^{2} + 2$

$\bf\large\underline\blue{Hence\:Proved.}$