Question

If x2+1\x2=14, find the value of x3+1/x3.

Answer 1

x² + 1/x² = 14

(x + 1/x)² -2.x.1/x = 14

(x + 1/x )² -2 = 14

(x + 1/x )² = 16

take square root both sides

(x + 1/x) = 4

then,

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

= ( x +1/x)³ -3(x + 1/x)

= (4)³ -3(4)

= 64 - 12

= 52

Answer 2

Hey there!

Given,

x² + 1/x² = 14

(x + 1/x)² - 2(x)(1/x) = 14

(x + 1/x)² = 14+2

(x + 1/x)² = 16

x + 1/x = √16

x + 1/x = 4

-----------------

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

= 4³ - 3(4)

= 64 - 12

= 52.

:)