Question

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

Answer 1

Answer:

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