SOLUTION: Please help me solve this question:Express the fraction 19/72 in the form 1/a + 1/b where a and b are positive integers.

Question 56723: Please help me solve this question:Express the fraction 19/72 in the form 1/a + 1/b where a and b are positive integers.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me solve this question:Express the fraction 19/72 in the form
1/a + 1/b where a and b are positive integers.
------------
1/a + 1/b = 19/72
(b+a)/ab = 19/72
EQUATIONS:
1st: a+b=19
2nd: ab=72
Solve 1st for a and substitute in 2nd:
a=19-b
(19-b)b=72
19b-b^2=72
b^2-19b+72=0
b=[19+-sqrt(19^2-4(72)]/2
b=[19+-sqrt(73)]/2
Comment: Notice that b is not an integer.
I have a sneaking suspicion that your
problem should read 1/a + 1/b = 17/72
and not what you have posted.
If I am right a=9 and b=8.
Cheers,
Stan H.

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