SOLUTION: If the sum of two numbers is 4 and the product of the numbers is 7, find the sum of the squares of the reciprocals of these numbers.
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Question 449686: If the sum of two numbers is 4 and the product of the numbers is 7, find the sum of the squares of the reciprocals of these numbers.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose the numbers are a,b with a+b = 4 and ab = 7. We wish to find
.
This is equal to
.
Right away, we know that since ab = 7, then a^2*b^2 = 49. We can find a^2 + b^2 by squaring a+b:
^2 = 4^2)
However we know that ab = 7, 2ab = 14, so
We substitute into our desired expression to get
.
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