anonymous
  • anonymous
The value of _____
Mathematics
katieb
  • katieb
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hartnn
  • hartnn
is _______
anonymous
  • anonymous
\[\sqrt{1 + 2008\sqrt{1 + 2009\sqrt{1 + 2010\sqrt{1 + 2011.2013}}}}\]
anonymous
  • anonymous
what is the value of the above ???

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Mimi_x3
  • Mimi_x3
do you have access to a calculator? or do you want to solve it by hand?
anonymous
  • anonymous
we are Indians and here most of the time its by hand ...so please try to solve and help me out without the use of calculator,,
hartnn
  • hartnn
ok, now can u write 2011*2013 as (2012-1)(2012+1) ?? and do u know what (a+b)(a-b) =??
anonymous
  • anonymous
yeah \[(a+b)(a-b)=a ^{2}-b ^{2}\]
hartnn
  • hartnn
good, so what will be (2012-1)(2012+1) =??
anonymous
  • anonymous
\[2012^{2}-1\]
hartnn
  • hartnn
and u had 1+ 2011*2013 so now whats 1+2012^2-1 ??
anonymous
  • anonymous
heyyyyy thaaaanzzznnzzzz buddy i got it all after dat ...u made it so easy 4 me now!!!...champ!!!..thnak u!
hartnn
  • hartnn
welcome :)
anonymous
  • anonymous
hey @sriramkumar u typing since long tym eh!
anonymous
  • anonymous
let 2012=a, then the problemn becomes \[\sqrt{1+(a-4)\sqrt{1+(a-3)\sqrt{1+(a-2)\sqrt{1+(a-1)(a+1)}}}}\] then the inner root becomes \[a ^{2}-1 +1=a ^{2}\] \[1+(a-2)\sqrt{a ^{2}}=1+(a-2)a=1+a ^{2}-2a=(a-1)^{2}\] ...... and so on....
anonymous
  • anonymous
damn gud!!!....@sriramkumar
anonymous
  • anonymous
n the answer is 2009

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