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FIND THE SQUARE ROOT OF (2011*2012*2013*2014)+1.

FIND THE SQUARE ROOT OF (2011*2012*2013*2014)+1.

Grade:10

3 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Sathyaram,

 

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 20012+3*2011+1 = 20011*2014+1 = 4030015.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

AMIN II
21 Points
10 years ago

wel...brother...i think this question appeared in F-NSTSE. Thought it looks complicated but its not that hard..lets see :

let 2011=x, Then 2012=(x+1), 2013=(x+2) & 2014=(x+3)

Then we have:

M = √x(x+1)(x+2)(x+3)+1            .... (say)

   =√[x(x+3)][(x+1)(x+2)]+1

  = √[(x2+3x)(x2+3x+2)]+1

  = √[(x2+3x+1)-1][(x2+3x+1)+1]+1

  = √[(x2+3x+1)2-12]+1

  = √(x2+3x+1)2-1+1

  =  √(x2+3x+1)2

  =  x2+3x+1 

Therefore, M = 20112 + 3(2011) +1 = 4,050,155

I hope this help u...:) 





Sathya
35 Points
10 years ago

I am studying in 10th standard.I want to talk to you through this website,how can i talk to you privately?Eager to know your reply.

Regards,

V.Sathyaram

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