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2011*2012*2013*2014*2015+1 find square root of the above number.



 2011*2012*2013*2014*2015+1
find square root of the above number.




Grade:12

2 Answers

Rishabh Raj
29 Points
9 years ago
let 2011=x then 2012=x plus 1 2013=x plus 2 2014=x plus 3 2015=x plus 4 Now proceed with this
Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Keshav,

 

Here's a solution, slightly tricky:

 

Let 2011 = x

So x(x+1)(x+2)(x+3) + 1 = (x2+3x)(x2+3x+2) + 1 = (x2+3x)2 + 2(x2+3x) + 1 = (x2+3x+1)2

So square root of that would be x2+3x+1

Where x = 2011.

Which is 20112+3*2011+1 = 2011*2014+1 = 4050155.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

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