SOLUTION: I am looking at how to solve 1/a + 1/b = 37/180 Can you explain this to me or tell me where to go to learn how to do this? Thank you, Nancy

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: I am looking at how to solve 1/a + 1/b = 37/180 Can you explain this to me or tell me where to go to learn how to do this? Thank you, Nancy      Log On


   

Question 182: I am looking at how to solve 1/a + 1/b = 37/180
Can you explain this to me or tell me where to go to learn how to do this?
Thank you,
Nancy
Answer by KMST(5484) About Me  (Show Source):
You can put this solution on YOUR website!
We know that solutions cannot have a=0 Or b=0
1%2Fa%2B1%2Fb=37%2F180 --> %28b%2Ba%29%2Fab=37%2F180 .
You could be tempted to think that the solutions are the solutions to system%28a%2Bb=37%2Cab=180%29 ,
but what about the solutions to
system%28a%2Bb=37k%2Cab=180k%29 for other possible values of k%3C%3E0 ?
The set of solutions is infinite.
With k=5, we get the solutions system%28a=5%2Cb=180%29 and system%28a=180%2Cb=5%29
With k=0.6 , we get system%28a=7.2%2Cb=15%29 and system%28a=15%2Cb=7.2%29 .
I found no other solution sets that looked that elegant,
or any rational numbers, except maybe
a=b=2%2A180%2F37=360%2F37=9.729729729...+ when k=720%2F1369=4%2A180%2F37%2F37

The way I found solution sets is
if system%28a%2Bb=37k%2Cab=180k%29 with k%3C%3E0, then a and b are solutions of
%28x-a%29%28x-b%29=0<-->x%5E2-%28a%2Bb%29x%2Bab=0<-->x%5E2-37kx%2B180k%2B0
and the solutions of the last equation can be calculated as

Two solutions exist when %281369k-720%29k%3E0-->system%28k%3E720%2F1396%2C%22or%22%2Ck%3C0%29
There is one solution when k=720%2F1369=4%2A180%2F37%2F37 and then a=b=37k%2F2=37%2A4%2A180%2F37%2F37%2F2=2%2A180%2F37=360%2F7+
What was the expected answer?
That the pairs of { %22a+%2C+b%22 } solutions can be found as
x=+%28-37k+%2B-+sqrt%28%281369k-720%29k%29+%29%2F2+ for system%28k%3E=720%2F1369%2Cor%2Ck%3C0%29 ?