Question

If a+b=3 and a^b+b^a=27 find a and b

Answer 1

First of all you have to find out the values of a and b.

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 cros 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