Question

If ab+b+a=135 bc+b+c=47 ca+a+c=101
then what is a+b+c

Answer 1

1+=8|1+=−81+b=8|1+b=−8 and 1+=6|1+=−61+c=6|1+c=−6

On solving

=16,=7,=5|=−18,=−9,=−7a=16,b=7,c=5|a=−18,b=−9,c=−7

So,

The answers are

++=28|++=−34

Answer 2

ab + b + a = 135

1 + ab + b + a = 135 + 1

(1 + a)(1 + b) = 136 --------------------- [  1 ]

bc + b + c = 47

1 + bc + b + c = 47 + 1

(1 + b) (1 + c) = 48 --------------------- [  2 ]

ca + a + c = 101  

1 + ca + a + c = 101  + 1

(1 + a) (1 + c) = 102 --------------------- [  3 ]

Putting all the 3 equations together:

(1 + a)(1 + b) = 136 --------------------- [  1 ]

(1 + b) (1 + c) = 48 --------------------- [  2 ]

(1 + a) (1 + c) = 102 --------------------- [  3 ]

[ 1 ] ÷ [ 2 } :

( 1 + a) / ( 1 + c) = 17/6 --------------------- [  4 ]

Find a: [ 3 ] x [ 4 ] :

(1 + a)² = 289

1 + a = 17

a = 16

Find b : Sub a = 16 into [ 1 ]:

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

(1 + 16)(1 + b) = 136

17( 1 + b) = 136

1 + b = 8

b = 7

Find c : Sub a = 16 into [ 2 ]:

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

(1 + 16) (1 + c) = 102

17( 1 + c) = 102

1 + c = 6

c = 5

Find a + b + c:

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

Answer: 28