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