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Let u and v be the solutions to 3x^2 + 5x = 7 = 0.  Find u^2 + v^2.

 Jun 18, 2021
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By Vieta's Theorem the equation $3x^2+5x=7=0$ gives you the values of $u+v$ and $uv$.   Noticing that $u^2+v^2 = (u+v)^2 - 2uv$ should tell you what to do.

 Jun 18, 2021

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