How do you find two consecutive positive odd integers whose product is 143?
Notice that consecutive odd integers will differ by
#143 = (n-1)(n+1) = n^2-1#
#n^2 = 144 = 12^2#
Since we are told that the integers are positive, use
Alternatively, just find factors of
11 and 13
Proceed as below.
Rest of the steps are same as followed by others.
It is by convention, as
Expanding on AO8's answer: This approach guarantees that any number we look at is odd:
We need to be able to guarantee that we are dealing with odd numbers.
Suppose n is even. Then
Suppose n is odd. Then
But in both cases
Let the first odd number be
Then the second odd number will be
We are given that the product is 143 so write the equation as:
This is saying exactly the same thing as the others but in a slightly different way! So we now have:
Divide by 4
So for my conditions
Thus the first number is:
So the second number is