+964 Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.
+1908 Let's first find u and v. Carrying all terms to one side and combining like terms, we get \(x^2-6x+13=0\)
Using the quadratic equation, we get \(x=3+2i,\:x=3-2i\), meaning we have \(u =3-2i\) and \(v =3+2i\).
Plugging these values into \(u/v^2 + v/u^2\), we get \(\frac{3-2i}{(3+2i)^2} + \frac{3+2i}{(3-2i)^2}\)
Simplifying the expression gets us the fraction \(-\frac{18}{169}\)
Thanks! :)
