Question

x²+1/x²=11 Find the value of x-1/x​

Answer 1

x-1=11x (Transposing x to RHS)

-1=11x -x

-1=10x

x= -1/10

Checking the value by substitution,

(-1/10)-1)/(-1/10)=11

(-11/10)/(-1/10)= 11

-11/10*10/-1= 11

11=11

(L.H.S = R.H.S)

Therefore, x=-1/10

((x+1)/x)^2

(((-1/10)+1)/(-1/10))^2

((9/10)/(-1/10))^2

(9/10*10/-1)^2

(-9)^2

81

So, ((x+1)/x)^2 = 81