SOLUTION: if the sum of two numbers is 10 and their product is 5 what is the sum of their reciprocals

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Question 911831: if the sum of two numbers is 10 and their product is 5 what is the sum of their reciprocals
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers, x and y;
x+y=10 and xy=5;
First goal is solve for x and y.

x%2810-x%29=5
-x%5E2%2B10x-5=0
x%5E2-10x%2B5=0 not factorable.

x=%2810%2B-sqrt%28100-4%2A5%29%29%2F2
x=%2810%2B-sqrt%2880%29%29%2F2
x=%2810%2B-%28sqrt%282%2A2%2A2%2A2%2A5%29%29%2F2
x=%2810%2B-4sqrt%285%29%29%2F2
highlight%28x=5%2B-2sqrt%285%29%29

highlight_green%28y=10-x%29
y=10-5%2B-2sqrt%285%29
highlight%28y=5%2B-2sqrt%285%29%29

x and y are equal. You will want to rationalize the denominators when looking for their reciprocal. Actually, one number (either x or y) would take the positive square root and the other number will take the negative square root.