Question

Ifp+1/p=5 then find the value of (P-1/p) ^2

Answer 1

i hope it will help u

Answer 2

Answer:

The value of  $(p-\frac{1}{p} )^{2}$ = 21.

Step-by-step explanation:

Given that p+ $\frac{1}{p}$ = 5

We know that (a + b)² = a²+b²+2ab

(a - b)² = a²+b²-2ab

$p+\frac{1}{p} =5$

Squaring on both sides

($p+\frac{1}{p}$)² = 5²

$p^{2} +(\frac{1}{p} )^{2} +2p\frac{1}{p}$ = 25

$p^{2} +(\frac{1}{p} )^{2} +2$ = 25

$p^{2} +(\frac{1}{p} )^{2}$ = 25 - 2 = 23

Now we find the value of $(p-\frac{1}{p} )^{2}$

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

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

            = 23 - 2

           = 21.

Therefore,  $(p-\frac{1}{p} )^{2}$ = 21.