The product of two, positive, consecutive integers is equal to 72. Find both internet's using an algebraic method.

8 and 9

Step-by-step explanation:

From the question we are given;

The product of two positive consecutive number is 72

We are required to determine the integers;

We need to know that the difference between two consecutive integers is 1 Therefore;

Assuming that the smaller integer is x

Then the other integer is x+1

Therefore;

x (x+1) = 72

x² + x = 72

Rearranging in quadratic manner;

x² + x - 72 = 0

Solving quadratically, using factor method;

Product = - 72x

Sum = x

Numbers = 9x and - 8x

Thus;

x² + 9x - 8x - 72 = 0

x (x+9) - 8 (x+9) = 0

Then;

(x-8) (x+9) = 0

Hence, x-8 = 0 or x+9 = 0

Therefore, x = 8 or x = - 9

We take, x = 8 (positive integer)

Hence, the required integers are 8 and 9