Question

find the value of x+1/X and x-1/x​

Answer 1

Heya

Q.NO 8 :-

1) Find x + 1/x

x² + 1/x² = 27 { Given }

let ( x + 1/x )= z

Squaring on both sides we have

( x + 1/x )² = z²

x² + 1/x² + 2 (x)× (1/x) = z²

Becoz ( a + b )² = a² + b² + 2ab

x² + 1/x² + 2 = z²

27 + 2 = z²

z² = 29

z = ±√(29)

z = ±3√3

So, x + 1/x = 3√3 or x + 1/x = -3√3

2) Find x - 1/x

let x - 1/x = y

squaring on both sides we have

( x - 1/x )² = y²

x² + 1/x² - 2(x)×(1/x) = y²

27 - 2 = y²

y² = 25

y = ±√(25)

y = ±5

So, x + 1/x = 5 or x - 1/x = -5