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Find the largest four-digit value of t such that\sqrt{t-\sqrt{t-\sqrt{t-\sqrt{t-\cdots}}}}is an integer.

Guest Jan 31, 2015

Best Answer 

 #1
avatar+889 
+10

Put the expression equal to N (an integer) and square it.

That gets you N^2 =  t- N  or, t = N^2 + N.

The largest integer value for N that can be substituted so that t is still a 4 digit numbe is 99 and that gets

you t = 9900.

Bertie  Feb 1, 2015
 #1
avatar+889 
+10
Best Answer

Put the expression equal to N (an integer) and square it.

That gets you N^2 =  t- N  or, t = N^2 + N.

The largest integer value for N that can be substituted so that t is still a 4 digit numbe is 99 and that gets

you t = 9900.

Bertie  Feb 1, 2015
 #2
avatar+92781 
+5

That is really neat Bertie  

Melody  Feb 1, 2015
 #3
avatar+87301 
0

Yes it is  !!!!

 

CPhill  Feb 1, 2015

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