SOLUTION: find two integers whose difference is 23 and whose product is 195

Question 67005: find two integers whose difference is 23 and whose product is 195
Found 2 solutions by ptaylor, stanbon:
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
find two integers whose difference is 23 and whose product is 195
CHECK YOUR NUMBERS----THE SOLUTIONS TO THIS PROBLEM ARE NOT INTEGERS.
Let x=larger integer
x-23=smaller integer
Now we are told that:
x(x-23)=195 clear parens
x^2-23x=195 subtract 195 from both sides:
x^2-23x-195=0
Using the quadratic formula, we get:
x=(+23+or-sqrt(529+780))/2;
x=(+23+or-sqrt(1309))/2;
sqrt(1309)=36.180 -----something is wrong!!!
x cannot be an integer
Hope this helps----ptaylor

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find two integers whose difference is 23 and whose product is 195
Let the integers by x and y
EQUATIONS:
x-y=23
xy=195
----------
Solve one for x: x=y+23
Substitute into the other to get:
(y+23)y=195
y^2+23y-195=0
Use the quadratic formula to get:
y=[-23+-sqrt(23^2-4*-195)]/2
y=[-23+-sqrt1309}/2
y=[-23+-36.18...]/2
This does not yield an integer.
You may have posted your numbers incorrectly.
Cheers,
Stan H.
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