Question

if x plus 1/ x equals to 3 then find the value of x ^6 plus 1/x^6

Answer 1

x+1/x = 3

(x+1/x)²=3²=9

⇒x²+1/x²+2=9⇒x²+1/x²=7

Cubing both sides,

x^6 +1/x^6 +3*x²*1/x²(x²+1/x²)=343

⇒x^6 + 1/x^6 = 322