Find the largest four-digit value of such thatis an integer.

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

Guest Jan 31, 2015

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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

Bertie · Answer 1 · 2015-02-01T10:15:32

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.

Melody · Answer 2 · 2015-02-01T10:42:08

That is really neat Bertie

CPhill · Answer 3 · 2015-02-01T10:45:40

Yes it is !!!!