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Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

 Mar 11, 2024
 #1
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Simplify as

 

x^2 + 10x -   4  =  0

 

Call the roots a,b

 

Product of roots  = ab  =   -4

Sum  of roots =   a + b =   -10    square both sides

a^2 + 2ab + b^2  = 100

a^2 + 2(-4) + b^2   =100

a^2 + b^2   - 8  = 100

a^2 + b^2  = 108

 

cool cool cool

 Mar 11, 2024

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