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!