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.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> 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.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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:



However we know that ab = 7, 2ab = 14, so



We substitute into our desired expression to get
.