Question

If a+b=12 and ab=27 find a 3 +b 3

Answer 1

a+b=12 (Given data) 
a= 12-b (By transposition) 

ab= 27 (Given data) 
a= 27/b (By transposition) 

=27/b= 12-b 
=27= 12b-b^2 (By cross multiplication) 
= b^2-12b+27=0 (By arranging the terms in standard form of quadratic equation) 
= b^2-9b-3b+27=0 (By splitting the middle term) 
= b(b-9)-3(b-9)= 0 
= (b-9)(b-3)= 0 
= b=9 b=3 

Let b=9. 
By substituting: 
a+9= 12 
a= 3 

Therefore a^3+b^3= 3^3+9^3 
= 27+729 
= 756

Hence     a^3+b^3 = 756   ans.

Answer 2

We know that (a+b)³=a³+b³+3ab(a+b)
Given that a+b=12 and ab=27
Substituting in (a+b)³=a³+b³+3ab(a+b),
12³=a³+b³+3(27)(12)
a³+b³=1728-972=756
Hence a³+b³=756.
Hope you find this answer helpful.