Greatest Integer X

If [X] represents the greatest integer function, then [X] represents the greatest integer less than or equal to X.  Find the value of X if the product of X and [X] equals 200.
Source: mathcontest.olemiss.edu 1/112010

SOLUTION
If X=14.25, then 14.25\times [14.25]=14.25\times 14=199.5.

If X=14.30, then 14.30\times [14.30]=14.30\times 14=200.2.

Let X=200\div 14=14.28571429, then
14.28571429\times [14.28571429]=14.28571429\times 14=200.

Answer: X=14.28571429.

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About mvtrinh

Retired high school math teacher.
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