Some square roots

Algebra Level 5

$X= \sqrt { a+\sqrt { b+\sqrt { c+\sqrt { d+X } } } }$

Let $a,b,c,d$ and $X$ be positive integers satisfying the equation above. Find the minimum value of $n > 2016$ , where $n$ is the 4-digit integer $\overline{abcd}$ .

The answer is 2167.

1 solution

Sal Gard
Jun 2, 2016

There are solutions less than 2016, so I'm glad this has been specified.

The answer is 2231 where X=0

Kunal Singhal - 5 years ago

First of all, 2167 is smaller. Second of all, this doesn't work. As x must be greater than or equal to 2.

Sal Gard - 5 years ago

Yes, n=1667 is the smallest solution for X=2. But X=2 has not been specified ! And if we consider X=1, then we have n=0 (not really interesting) :-\ . This is why n must be greater than 2016 ;-) . (I'm sorry if my bad english hurt you :-P )

Abysse Synus - 5 years ago

It is also the smallest overall. After the domain of three, this is not even possible considering we have a four digit number out of the digits. 1667 is in fact the smallest overall, followed by 1672.

Sal Gard - 5 years ago

Some square roots

The answer is 2167.

1 solution

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