if α+β =4 and α3+β3=44 then α,β are the roots of the equation
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we have two equations,
a + b = 4 and a^3+b^3 = 44
we can write,
(a+b)^3 - 3ab(a+b) = 44
and we know, a+b = 4
hence, we have 64 - 12ab = 44
=> 12ab = 20
=> 3ab = 5
=> 3a(4-a) = 5
=> -3a^2 + 12a = 5
=> 3a^2 -12a + 5 = 0
by solving this we have,
a = 3.5 or 0.5
a = 3.5 or 0.5b = 0.5 or 3.5
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