Question

if p + ¹/p = 11, find (i)p² + ¹/p² (ii) p² - ¹/p²

Answer 1

Hey ,

here is ur answer

(i) if p + 1/p = 11

then p square + 1/p square = 11 square

p square + 1/p square = 121

(ii) if p + 1/p = 11

then p - 1/p = -11

p square - 1/p square = -11 square

p square - 1/p square = 121

Answer 2

Answer:

p² + 1/p²  = 119

p²-1/p² = 11*√117

Step-by-step explanation:

p + 1/p = 11

Square both Sides

p² + 1/p² + 2*p*1/p = 121

p² + 1/p² +2 = 121

p² + 1/p²  = 119

to get value of

p² - 1/p²

Multiply p-1/p both side to given

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

p²-1/p² = 11(p-1/p)   - Eq A

now to get p-1/p value

(p-1/p)² = p²+1/p²-2

(p-1/p)² = 119-2  ( value from 1st solution)

(p-1/p)² = 117

so p-1/p = √117

put this value in Eq A

p²-1/p² = 11*√117