Question

If (x-1/x)=8 find the values of 1. (x+1/x)

Answer 1

x-1/x=8

=>(x-1/x)^2=8^2

=>x^2+(1/x^2)-(2×x×1/x) = 64

=>x^2+(1/x^2)-2= 64

=>x^2+(1/x^2)= 64+2=66 ------(i)

Now, (x+1/x)^2=x^2+(1/x^2)+(2×x×1/x)

=>(x+1/x)^2=66+2 [Using (i)]

=>(x+1/x)^2=68

=>x+1/x = 68^1/2 = 2×sqrt17

I hope my ans helps