The product of two consecutive odd integers is 143. How do you find the integers?
11 and 13.
Call x a number
The number (2x + 1) should be an odd number no matter what x is.
The consecutive odd number to (2x + 1) will be: (2x + 3).
(2x + 1)(2x + 3) = 143
Solve this quadratic equation for x. Find 2 numbers knowing sum (-2) and product (-35). They are x = 5 and x = -7 (rejected as negative)
The odd number is N = (2x + 1) = 10 + 1 = 11
The consecutive odd number is: N + 2 = (2x + 3) = 10 + 3 = 13
Their product is (11 x 13) = 143. OK
Then we have:
#143 = (n-1)(n+1) = n^2-1#
#144 = n^2#
The consecutive odd numbers must lie on either side of the square root of 143
Look for odd numbers either side of
Remember the factors could be negative as well..
If you write the factors of a number in increasing order, note the following:
Factors are always in pairs.
- The difference between the factors is greatest for the outside factors and least for the innermost factors.
For example the factors of 48 are:
48- 1 = 47 but 8-6 = 2
- The square root of a number is exactly in the middle of the factors
For example the factors of 36 are