Question

If ab + b + a = 135 ; bc + b + c = 47 ; ca + a + c = 101 what is the value of a + b + c?

Answer 1

"If,

(1) ab + b + a = 135

(2) bc + b + c = 47

(3) ca + a + c = 101

adding one on both side of (1)

ab + b + a + 1 = 136

(1 + a) (1 + b) = 136, (3)

Similarly, add one in (2)

bc + b + c + 1 = 48

(1 + b) (1 + c) = 48 (4)

Similarly with (3)

(1 + c) (1 +a) = 102 (5)

Now let,

(3)/(4) * (5)

(1+a) (1+b) * (1+c) (1+a) / (1+b) (1+c) = 136 * 102/48

(1+a)^2 = 17^2

(1+a) = 17, a = 16

Similarly, 1+b = 8, b =7 and 1+c = 6, c = 5

Hence, a + b + c = 16 + 7 + 5 = 28

"