Question

1. If 2x+1/x=2, find the value of x/(2x²+x+1)

Answer 1

Solving the given equation for x, we find two complex roots to the quadratic equation x^2 - x + 2 = 0:

x = (1 +/- sqrt(7)*i)/2

And

x^2 = (-3 +/- sqrt(7)*i)/2

We can simplify x^2 + x + 2*(1 - x)/x^2 by replacing x with x^2 + 2 to get:

2*(x^2 - 1/x^2)

Substituting the known values for x^2 we get:

(-9 +/- 5*sqrt(7)*i)/4