Quant Question Of The Day : 3

Algebra

If a, b and c are positive real numbers such that ab + a + b = bc + b + c = ca + c + a = 35. Find the value of (a + 1) (b +1)(c+1) .

Adding 1 to both sides of the given equation ab + b + a = 35 , we get

ab + b + a + 1 = 36

a (b + 1) + 1 ( b +1) = 36

(a + 1) (b +1) = 36

likewise adding 1 to the other two equation gives (b +1)(c+1) = 36 and (c+1)(a+1) = 36

Now multiplying the three resulting equations above leads to [ (a+1)(b+1)(c+1)]² = 36³

[ (a+1)(b+1)(c+1)]² = 6⁶

It follows (a+1)(b+1)(c+1)= 6³ = 216