Question

if α+β =4 and α3+β3=44 then α,β are the roots of the equation​

Answer 1

Answer:

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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