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#1

$Old$ September 30th, 2009, 09:42 AM

anshulbshah $anshulbshah is offline$

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$Question$ Help me with this sum...

For which real no. a the equation x^2-(a-2)x-(a+1)= 0 has the least value of sum of the squares of its roots?

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#2

$Old$ September 30th, 2009, 11:59 AM

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$x_1^2+x_2^2=(x_1+x_2)^2-2x_1x_2=$

$=(a-2)^2+2(a+1)=a^2-2a+6=(a-1)^2+5$

The minimum is 5, for a=1.

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