Question

If x - 1/x = 3, find the value of x^4 + 1/x^4​

Answer 1

Answer:

x-1/x=3

(x-1/x) ^2=(3) ^2 [Squaring both sides]

(x) ^2+(1/x) ^2-2*x*1/x=9 {since, (a-b) ^2=a^2+b^2-2ab)}

x^2+1/x^2-2=9 ( since, x and 1/x will get cancelled)

x^2+1/x^2=9+2

Therefore, x^2+1/x^2=11

(x^2+1/x^2) ^2=(11) ^2 [Squaring both sides]

(x^2) ^2+(1/x^2) +2*x^2*1/x^2=121

x^4+1/x^4+2=121

x^4+1/x^4=121-2

Therefore, x^4+1/x^4=119 ( Ans)