maths
posted by njovu .
Given that the roots of 2x^24x+5 are alpha and beta,find the value of ...
(i)alpha^3beta^3
(ii)(alphabeta)^2

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....
(ab)^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
(ab)^2 = (a+b)^2  2ab  2ab