Question

value of p^2+1/p^2 if p-1/p=9​

Answer 1

$\large\underline{\underline\mathrm\red{QUESTION}}$

Find the value of

$\bold{p²+\frac{1}{p²}}$ if $\bold{p -\frac{1}{p}=9}$

$\large\underline{\underline\mathrm\green{SOLUTION}}$

GIVEN

$\bold{p -\frac{1}{p}=9}$......(1)

FORMULA

$\bold{(a-\frac{1}{a})²= a²+\frac{1}{a²}-2}$

From equation (1)

$\bold{p -\frac{1}{p}=9}$

Squaring on both side, we get

$\bold{\implies(p -\frac{1}{p})²=(9)²}$

$\bold{\implies p² + \frac{1}{p²} -2 =81}$

$\bold{\implies p² + \frac{1}{p²} =81+2}$

$\bold{\implies p² + \frac{1}{p²} =83}$

Therefore

$\bold{\implies p² + \frac{1}{p²} =83}$

Answer 2

Answer:

83

hope it is helpful to you