Posted by njovu on Tuesday, March 13, 2012 at 7:40am.
Using the sum and product of roots property, we know
a+b = - (-4/2) = 2 and ab = 5/2, where a and b are alpha and beta
we know that
(a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2
(a+b)^3 = a^3 + b^3 + 3ab(b+a)
2^3 = a^3 + b^3 + 3(5/2)(2)
8 = a^3 + b^3 + 15
a^3 + b^3 = -7
in the same way....
(a-b)^2 = a^2 - 2ab + b^2
= a^2 +b^2 - 2ab
but a^2 + b^2 = (a+b)^2 - 2ab
so
(a=b)^2 = (a+b)^2 - 2ab - 2ab
= 4 - 5/2 - 5/2
= -1
in the third last line I should have had
(a-b)^2 = (a+b)^2 - 2ab - 2ab
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