The product of two consecutive odd integers is 143. How do you find the integers?
Answers
Answered by
7
11 and 13.
Exp
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).
There for:
(2x + 1)(2x + 3) = 143
4
x
2
+
6
x
+
2
x
+
3
=
143
4
x
2
+
8
x
−
140
=
0
x
2
+
2
x
−
35
=
0
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
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