Question

3^a×2^b=72,then calculate a + b​

Answer 1

Step-by-step explanation:

a^3+b^3=72=>b^3=72-a^3

a^2-b^2=12=>a^2-12=(72-a^3)^2/3

=>(a^2-12)^3=(72-a^3)^2

=>a^4-4 a^3-12 a^2+192=0

It is easy to see this equation is satisfied by a=4.

Thus (a-4) is a factor of a^4-4 a^3-12 a^2+192=0

Thus (a-4)(a^3 - 12 - 48 )=0=>a=4 or a^3-12 a^2+192=0

Hence one possible value of a and b are a=4 and b=2.

For other solution consider a^3 - 12 a^2+192=0.This equation

has only one real solution. you can find other possible solution

a+b=6