SOLUTION: The problem is : 2 positive numbers that differ by 7 whose product is 1 I have not been able to come up with an answer.
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Question 4403: The problem is : 2 positive numbers that differ by 7 whose product is 1 I have not been able to come up with an answer.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = first number
y = second number
Write two equations based upon the first two sentences.
x-y = 7
xy = 1
Solve for x in the first equation by adding +y to each side.
x-y = 7
x-y+y= 7 + y
x = 7+y
Substitute x = 7+y into the second equation for x:
xy = 1
(7+y)y = 1
Next use the distributive property, and since a quadratic equation results, set it equal to zero.
This obviously does not factor, which may be why you had a problem with it. There are no whole number solutions that work!! Use the quadratic formula to solve it:
, where a= 1, b=7, c=-1
It appears that there are two solutions
and .
However, according to the problem, these must be POSITIVE numbers, which rules out the second above.
The solution is
and
or
or =
To check, show that their difference is 7 and their product is 1. (I sure don't want to post this so everyone can see, until I make sure that it works!!)
Difference = -
Difference = = =
Product = FOIL this out!!
=
Final Answer: ,
R^2 at SCC
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