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The sum of two numbers is 4 and their product is 2. What is the sum of their reciprocals?
Its been a VERY long time since I've done any Algebra or higher math. I'm working on a sample problem I need to apply to others. I know that in order to go about solving it, the Sum of two Numbers is 4 would look like X+Y=4. The Product part would look like X*Y= 2. This is as far as I can get. Can someone explain step by step where to go from here?
1 Answer
- 1 decade agoFavorite Answer
You are on the right track. You will begin with a system of equations: x + y = 4 and also x(y) = 2.
For the first equation, x + y = 4, if you solve for y you obtain the answer y = 4-x. Then, plugging this into the 2nd equation, you now have x(4-x) = 2.
When you multiply this out you get 4x - x^2 = 2. Then, solving for zero, you get: 0 = x^2 - 4x +2. It is now important to complete the square.
In completing the square, you obtain 2 = x^2 - 4x +4, which can be broken down to: 2 = (x-2)^2. You are now left with the answer that x = sqr root 2 + 2. which gives the final answer of:
99.