Question

if (2a+3b) =9 and ab=3 then the value of 8a+27b

Answer 1

(2a+3b)=9
ab=3
b=3/a

2a+3.3/a=9
2a+9/a=9
2a^2+9=9a
2a^2-9a+9=0

use quadratic formula ,

a={9+_3}/4=3,3/2

hence, b=1,2
so,
a=3,3/2 and b=1,2

now,
8a+27b=24+27=51
or
=12+54 =66

Answer 2

2a+3b=9----(1)
ab=3
b=3/a---(2)
Put b value in (1)
2a+3*3/a=9
2a^2+9=9a
2a^2-9a+9=0
2a^2-3a-6a+9=0
a(2a-3)-3(2a-3)=0
(2a-3)(a-3)=0
Therefore
2a-3=0 or a-3=0
a=3/2ora=3
Put these a values in (2)
b=3/(3/2)=2 or b=3/3=1
Now if a=3/2,b=2
8a+27b =8*3/2+27*2=12+54=66
Or
If a=3,b=1
8a+27b=8*3+27*1=24+27=51