Hi, I'm having trouble with this question: Find the equation whose roots are the squares of the reciprocals of the roots of x^2+6x-2.

So far, I've done:

Let x1 and x2 represent roots of the original equation.

x1 + x2= -b/a

= -6

(x1)(x2) = c/a

= -2

Then I figured the roots of the required equation would be (1/x1^2) and (1/x2^2)

So the product of the required equation would be 1/4. However, I'm having difficulty finding the sum. I think it should be:

x1^2 + x2^2

___________

4

However, I don't know how to fix the numerator so that I can sub a value into it and get the correct sum. (Then obviously, I can just sub the sum and product into x^2-x[sum]+product). I thought of square-rooting the entire equation, but that doesn't work out. Any help finding the sum for the required equation would be greatly appreciated

Thank you!