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Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 + 11x - 6. Find u/v^2 + v/u^2.

 May 20, 2024
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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! :)

 May 20, 2024

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