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```        If for a particular day of the year, it happens that the sum of the date and square root of the month gives the
square of the month, then the date is:?```
6 years ago

Mayank Jain
37 Points
```										Let the day be x and the month be y
so 0<x<31 and 0<y<12 and x, y ε N (x and y are natural no.s)
Now given condition tells us that
x+√y=y2
so we get x=√y [y√y - 1]
But x is a natural no. so y has to be a perfect square
Hence possible values of y=1, 4, 9
taking y=1 we get x=1(1x1-1)=0   but x cannot be 0 so y is not 1
taking y=9 we get x=3(3x9-1)=78 but x cannot be more that 31
hence only y=4 is correct and then x=2(2x4-1)=14

Hence the final anwer will be 14th of April is the day that satisfies the given condtions.
```
6 years ago
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