Find the number of ordered triplet (a,b,c) of positive integers which satisfy simultaneous equations ab+bc=44 and ac+bc=23

Dear manoj,

ab + bc =  44

b(a+c) = 44

similarly c(a+b) = 23

since 23 is a prime number, c should be either 1 or 23

c cannot be 23 as a+b = 1 which is not possible as a and b are + integers.

so c =1

so by trail and error method u can find a and b

b = 2,  a = 21 as these two values satisfy the 1st equation: ab+bc=44

21*2+2*1=42+2=44

a=1and b=22 is one more solution