Question 594474: The sum of two integers is 9 and their product is 18. What are the integers?
Answer by mamiya(56)   (Show Source):
You can put this solution on YOUR website! let x and y be those integers.
by understanding the question, we know that x*y=18 and x+y=9
There are many ways to do this ( especially because 9 and 18 are small numbers).
First, let's take one of the easiest ways
we need to find two numbers whose sum is 9 , we have (1, 8) (2, 7) (3, 6) (4, 5)
Now, we look for the pair of numbers whose product is 18. Among those pairs of numbers, the only one satisfying our need is (3, 6) so 3 and 6 are those integers.
so, the answer is 3 and 6
Second way:
we need to find two numbers whose product is 18, we have (1, 18) (2, 9) (3, 6)
Now, we look for the pair of numbers whose sum is 9. Among those pairs , the only one satisfying our need is (3, 6).
so, the answer is 3 and 6
Another way :
x* y = 18, x+y = 9
consider x+y=9 and write one letter in term of the other one
x+y=9 --> x = 9 - y
now we plug that in the other equation
x*y = 18 --> (9-y)y = 18
--> 9y - y^2 = 18
--> y^2 -9y + 18 = 0
y = ( 9 - sqrt(9^2 -4(18)))/2
= ( 9 -sqrt(81 -72))/2
= ( 9 -sqrt9)/2
= (9-3)/2
= 3
y = ( 9 + sqrt(9^2 -4(18)))/2
= ( 9 + sqrt(81 -72))/2
= ( 9+ sqrt9)/2
= (9+3)/2
= 6
With this approach the answer are still 3 and 6
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