What two positive consecutive integers have a product of 72?
a = first mumber
b = second number
b = a + 1
a ∙ b = 72
a ∙ ( a + 1 ) = 72
a² + a = 72
a² + a - 72 = 0
The solutions are:
a = - 9 and 8
For a = - 9
b = a + 1 = - 9 + 1 = - 8
For a = 8
b = a + 1 = 8 + 1 = 9
The solutions are:
a = - 9 , b = - 8
and
a = 8 , b = 9
( - 9 ) ∙ ( - 8 ) = 72
8 ∙ 9 = 72
To find two positive consecutive integers with a product of 72, we can start by realizing that the numbers have to be close to the square root of 72. The square root of 72 is approximately 8.49, so let's consider the possible integers 8 and 9.
The product of 8 and 9 is 72, so these are the two positive consecutive integers we are looking for. Therefore, the answer is 8 and 9.
To find two positive consecutive integers with a product of 72, you can start by listing the factors of 72.
The factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
To determine the two positive consecutive integers, you need to find the factors that are consecutive. Looking at the list, we can see that the factors 8 and 9 are consecutive.
Thus, the two positive consecutive integers that have a product of 72 are 8 and 9.