Question

x squqre + 1/x square is equal to 14 find the value of x cube + 1/x cube

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

$x^2+1/x^2=14\\\\=x^2+1/x^2+2*x*1/x=16\\\\Now (x+1/x)^2=16\\\\x+1/x=4 or x+1/x=-4\\\\(x+1/x)^3=4^3\\\\=x^3+1/x^3+3*x*1/x(x+1/x)=64\\\\=x^3+1/x^3+3*4=64[x+1/x=4]\\\\=x^3+1/x^3=64-12=52$

Found the value.

Hope it helps.