Question

If x^2+1/x^2=14 Find x^3+1/x^3 with the positive value of X+1/x

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