Question

P^2 + 1/P^2= 11 ,find the value of p-1/p

Answer 1

Explanation:

p^2 + 1/p^2 = 11

(p - 1/p)^2 + 2(p)(1/p) = 11

(p - 1/p)^2 + 2 = 11

(p - 1/p)^2 = 11 - 2

(p - 1/p)^2 = 9

p - 1/p = ±√9

p - 1/p = ± 3

Answer 2

$HEYA \: \\ \\ GIVEN \: \: QUESTION \: Is \: \: \\ \\ p {}^{2} + \frac{1}{p {}^{2} } = 11 \: \: \: \: \: \: find \: \: p - \frac{1}{p} \\ \\ let \: \: \: \: p - \frac{1}{p} = z \\ squaring \: on \: both \: sides \: w e \: have \\ \\ (p - \frac{1}{p} ) {}^{2} = z {}^{2} \\ \\ p {}^{2} + \frac{1}{p {}^{2} } - \frac{2p}{p} = z {}^{2} \\ \\ 11 - 2 = z {}^{2} \\ \\ z {}^{2} = 9 \\ \\ z = \sqrt{9} \: \: \: or \: \: \: z = - \sqrt{9} \\ \\ z = 3 \: \: \: or \: \: \: z = - 3 \\ \\ therefore \: \: \: \: p - \frac{1}{p} = 3 \: \: or \: \: \: p - \frac{1}{p} = - 3$