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What are two consecutive even integers such that the sum of their reciprocals is 5 divided by 12?
Wiki User
∙ 13y ago
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Vivien Lind
Wiki User
∙ 13y ago4 and 6: 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Here's how to figure it out:
Two equations are:
- 1/x + 1/y = 5/12
- y = x+2
Solve for x and y:
- 1/x + 1/(x+2) = 5/12
- (2*x+2)/(x^2 + 2x) = 5/12
- 12*(2*x+2) = 5*(x^2 + 2*x)
- 5*x^2 + 10*x - 24*x - 24 = 0
- 5*x^2 - 14*x - 24 = 0
Use the quadratic formula to solve x = {4,-1.2}
The constraint that the numbers must be even integerseliminates -1.2,
so x = 4. Plug x=4 into equation #2 above, and y = 6.
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