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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

Best Answer 

 #1
avatar+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
avatar+2448 
0
Best Answer

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

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