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# Algebra

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90
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Find the sum of the squares of the solutions to 2x^2+4x-1=x^2+7x-3.

Jun 6, 2022

#1
+2448
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Moving everything to the right-hand side gives us: $$x^2 - 3x + 2 = 0$$

Let a and b be the roots of the quadraitc.

Now, recall the identity: $$a^2 + b^2 = (a+b)^2 - 2ab$$

By Vieta's, we know that $$a + b = -{ b\over a} = 3$$ and $$ab = {c \over a} = 2$$.

Can you take it from here?

Jun 6, 2022

#1
+2448
0

Moving everything to the right-hand side gives us: $$x^2 - 3x + 2 = 0$$

Let a and b be the roots of the quadraitc.

Now, recall the identity: $$a^2 + b^2 = (a+b)^2 - 2ab$$

By Vieta's, we know that $$a + b = -{ b\over a} = 3$$ and $$ab = {c \over a} = 2$$.

Can you take it from here?

BuilderBoi Jun 6, 2022