Question

Find number of ordered pairs of a and b such that a+b+ab = 119
where a and b are positive
integers.​

Answer 1

Answer:

14

Step-by-step explanation:

a + b + ab = 119

a + b + ab + 1 = 120

a(1+b) + 1+b = 120

(a+1)(b+1) = 120

So by factorising 120 = 1×2×2×2×3×5

a+1, b+1 = 1,120 ; 2,60 ; 3,40 ; 4,30 ; 5,24 ; 6,20 ; 8,15 ; 10,12 and their opposites ( eg. opposite of 10,12 = 12,10 )

so a,b = 0,119.....and so on

but a,b are positive so not = 0 so 0,119 and 119,0 are ruled out.

Hence (a,b) = (1,59), (2,39), (3,29), (4,23), (5,19), (7,14), (9,11) and their opposites.

So total 7 + 7 = 14 cases

Phew...

Hope it helps

Cheers