Question

if x^2+1/x^2=51,find x-1/x. 2). x^3-1/x^3​

Answer 1

Answer:

+/-7

+/- 364

Step-by-step explanation:

let x-1/x = t

t^2 = x^2 - 2 + 1/x^2 = 51 - 2 = 49

t = +/- 7 = x-1/x

x^3 - 1/x^3 = (x-1/x)(x^2+1+1/x^2)=+/-7 * 52 = +/- 364

Answer 2

it is given that, x² + 1/x² = 51

we have to find (1.) x - 1/x and (2.) x³ - 1/x³

now, x² + 1/x² = 51

or, (x - 1/x)² + 2x.1/x = 51

[ as we know, (a - b)² + 2ab = a² + b² ]

or, (x - 1/x)² + 2 = 51

or, (x - 1/x)² = 49 = (7)²

taking square root both sides,

or, (x - 1/x) = ± 7

hence, (x - 1/x) = 7 or -7

now, x³ - 1/x³ = (x - 1/x)³ + 3x.1/x(x - 1/x)

[ as we know, a³ - b³ = (a - b)³ + 3ab(a - b)]

= (x - 1/x)³ + 3(x - 1/x)

= (7)³ + 3(7)

= 343 + 21

= 364

similarly putting (x - 1/x) = -7

then, x³ - 1/x³ = (-7)³ + 3(-7)

= -364

hence, (x³ - 1/x³) = 364 or -364