The product of two consequtive postivite integers us equal to eleven times the sum of thw two integers plus 35. find the integers

We can represent the consecutive numbers with x and x+1.

Next, we can translate the sentences into an equation, factor, and solve for x.

x (x+1) = 11 (x + x + 1 + 35)

x^2 + x = 11 (2x + 36)

x^2 + x = 22x + 396

x^2 - 21x - 396 = 0

(x + 12) (x - 33) = 0

Since the question is asking for a positive no. we know the first integer must be 33. The next integer would be 34 because it is 1 more than 33.