How to find the sum of an integer and its reciprocal
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Suppose the sum of an integer and its reciprocal is 65/8. What is the integer?
Integer is a,
reciprocal is 1/a.
a + 1/a = (a^2+1)/a
a^2+1 = 65
a = 8
The method is to start by naming the thing you don't know, which is the integer. I called it "a". A reciprocal is an inverse and is 1/a.To add a and 1/a you must first get a common denominator, so a becomes a^2/a and you can add a^2/a to 1/a because you have a common denominator of a. The numerator becomes a^2+1 and the denominator is a.
At this point I noticed that in the original question the numerator is 65, which is 8^2+1, and the denominator is 8, which is a, and the problem is solved.
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Boo 17 months ago
I don't understand yèt :-x