Question

There are three consecutive positive integers such that if the square of the first increased by the product of the other two it gives 154. What are the integers?

Answer 1

Let the integers be x, x + 1 and x + 2.

Then, according to the question, $x^2$ + (x + 1)(x + 2) = 154.

$\Rightarrow 2x^2+3x-152=(2x+19)(x-8)=0$

It gives $x=-\frac{19}{2},8$

Since it is given that integers are positive.

Therefore, three consecutive integers are $8,9,10.$