SOLUTION: if a,b are positive numbers such that a+b=1 , prove that, 1/a+1/b >= 4

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Question 1016894: if a,b are positive numbers such that a+b=1 , prove that, 1/a+1/b >= 4
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fa+%2B+1%2Fb+=+1%2Fa+%2B+1%2F%281-a%29+=+1%2F%28a%281-a%29%29.
Now to minimize the last expression 1%2F%28a%281-a%29%29, we have to maximize a%281-a%29+=+-a%5E2+%2B+a
The maximum value of -a%5E2+%2B+a is C+-+B%5E2%2F%284A%29+=+0+-+1%5E2%2F%284%2A-1%29+=+1%2F4.
Therefore the minimum of 1/a + 1/b is 4, the inverse of 1/4.