X^-2 + x^-1 -110 =0

Question

Solve the equation by making an appropriate substitution 

Answer 1

This looks like a quadratic equation.  If we rewrite this in another way, we get

 

(x^-1)² + (x^-1) - 110 = 0

 

 

From this equation, we can say

 

Let        q = x^-1 = 1 / x

 

 

q² + q - 110 = 0

 

 

Factor the left side using FOIL.

 

(q + 11)(q - 10) = 0

 

 

Set the factors equal to zero and solve for q from each.

 

q = -11            and          q = 10

 

 

Substitute these values of q into the original substituted statement.

 

1 / x = -11              and              1 / x = 10

 

 

Now solve for x.  Can you continue from here?