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Find two numbers which are reciprocals of each other and whose sum is 3
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Let x be one of the two numbers.
Then the other number is (reciprocal !) and their sum is 3:
= 3.
We need to solve this equation to find x.
Multiply both sides by x to rid the denominator. You will get
= , or
= .
Apply the quadratic formula:
= = , or
= , = .
Check that the product = 1 and that = 3.
Answer. The two numbers are and .
