Question

If abc + ab + ac + bc + a +b+c = 4198 then a +b+cis.​

Answer 1

Thus, a + b + c = 46

Step-by-step explanation:

We are given as;

• abc + ab + ac + bc + a +b+c = 4198

• And, we are asked to find out the value of a + b + c.

We know already the standard formula as;

• (a + 1) (b + 1) (c + 1) = a + b + c + ab + bc + ca + abc + 1

We can rewrite as;

(a + 1) (b + 1) (c + 1) - 1 = a + b + c + ab + bc + ca + abc  ....(1)

• From the question, we have the value of the expression as;

• a + b + c + ab + bc + ca + abc = 4198

• Put the value of above expression in equation (1).

• (a + 1) (b + 1) (c + 1) - 1 = 4198

By simplifying it, we can write as;

• (a + 1) (b + 1) (c + 1) = 4198 + 1

Therefore, we get.

• (a + 1) (b + 1) (c + 1) = 4199

        (a + 1)(b + 1)(c + 1) = $13\times 17\times 19$

        (a + 1) (b + 1) (c + 1)  = (12 + 1) (16 + 1) (18 + 1)

Therefore; a = 12, b = 16, c = 18

Thus, a + b + c = 46