Find two consecutive positive integers whose product is 72
You should only have to think for an instant, remembering your times table, to find that 8x9=72
To find two consecutive positive integers whose product is 72, we can set up an equation representing this problem.
Let's represent the first integer as x. The next consecutive integer will be x + 1.
According to the problem, the product of these two integers is 72. So, we can write the equation as:
x * (x + 1) = 72
To solve this equation, we can expand and rearrange it:
x^2 + x = 72
Now, let's bring all terms to one side to get a quadratic equation:
x^2 + x - 72 = 0
This equation can be factored or solved using the quadratic formula.
Factoring the quadratic equation gives us:
(x + 9)(x - 8) = 0
Setting each factor equal to zero gives us two possible solutions:
x + 9 = 0 or x - 8 = 0
Solving these equations, we find:
x = -9 or x = 8
Since we are looking for positive integers, the solution is x = 8.
Therefore, the first positive integer is 8 and the next consecutive positive integer is 8 + 1 = 9.
So, the two consecutive positive integers whose product is 72 are 8 and 9.