Question

Advanced: a,b,c are positive numbers such that a+b+ab= 8, b+c+bc=15 and c+a+ca = 35 What is the value of a+b+c+abc?

Answer 1

Answer:

it can be solved by polynomials rule no. 2nd hope it helps you ;-)

Answer 2

Step-by-step explanation:

According to the question, there are 3 equations given:

a+b+ab= 8-----(i)

b+c+bc=15------(ii)

c+a+ca = 35---------(iii)

Now adding 1 to both the sides of equ (i) we get,

a+b+ab+1= 8+1

or, (a+1)(b+1)=9.

Similarly we get, (b+1)(c+1)=16 and (a+1)(c+1)=36.

now starting from the second equation,

We know that 16 has many factors but we have to brute force for satisfying the equation.

We know, 16 = 2 * 8 = (1+1) * (7+1) now, comparing it with equ(ii) we get, b=1,c=7.

Now putting the value of c in any two of the remaining equation we get,

(a+1)*(c+1)=36

or, (a+1)*(7+1)=36

or,(a+1) = 36/8 = 4.5

or, a = 4.5 - 1 = 3.5.

Now, a+b+c+abc = 3.5 + 1 + 7 + 3.5*1*7 = 36. [Ans]

I hope it's help you