Dr.Math --the smallest real number -- problems of the week
바로 콕 찍어서 - 진너자하/詩처럼아름다운數學 2007/05/25 15:45What is the smallest real number
which can be expressed
as the sum of the square root of 3x+4
and the square root of 5x+6 (where x is some real number)?
[SECRET]
Q: 가장작은을 뜻하는 영어 단어는?
A:smallest
[solution]
Since both 3x+4 and 5x+6 are increasing functions,
the minimum of the sum of square roots
will occur when both 3x+4 and 5x+6 are smallest
(subject to the requirements of the square root).
We will need both 3x+4 and 5x+6 to be nonnegative,
so that the smallest x allowed will be -6/5.
This gives the smallest real number expressible
as this sum of square roots to be the square root of 2/5
(we could write (2/5)^(1/2)=10^(1/2)/5 using ^ to mean "to the power".)
[/SECRET]
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