SOLUTION: the sum of two numbers is 20 and their product is 75 what is the sum of their reciprocal please solve it

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Question 889115: the sum of two numbers is 20 and their product is 75 what is the sum of their reciprocal please solve it
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be +a+ and +b+
(1) +a+%2B+b+=+20+
(2) +a%2Ab+=+75+
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(1) +b+=+20+-+a+
Substitute this into (2)
(2) +a%2A%28+20+-+a+%29+=+75+
(2) +20a+-+a%5E2+=+75+
(2) +a%5E2+-+20a+%2B+75+=+0+
I see by looking at this:
(2) +%28+a+-+5+%29%2A%28+a+-+15+%29+=+0+
+a+=+5+
and
(1) +b+=+20+-+a+
(1) +b+=+15+
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+1%2F5+%2B+1%2F15+=+3%2F15+%2B+1%2F15+
+1%2F5+%2B+1%2F15+=+4%2F15+ answer
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If I had chosen
+a+-+15+=+0+
+a+=+15+
then +a+ and +b+
just swap places