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avatar+973 

 

For how many real values of x is \(\sqrt{120-\sqrt{x}}\) an integer?

 Aug 11, 2018
 #1
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How convenient, you don't care when others tell you that you are being lazy and ungrateful, but when you need us to do your homework you ask for our help. Start responding to the comments on your previous questions.

 Aug 11, 2018
 #2
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+1

There are 11 real values of x as follows:

{x = 14400, x = 14161, x = 13456, x = 12321, x = 10816, x = 9025, x = 7056, x = 5041, x = 3136, x = 1521, x = 400}

 Aug 11, 2018
 #3
avatar+98129 
+1

y  = √ [ 120 - √x ]      where  y is an  integer

 

Note that   120 - √x  must be   ≥  0

 

One way of solving this is with a graph : https://www.desmos.com/calculator/xmrvja05tc

 

x values     y  values

14400              0

14161              1

13456              2

12480              3

10816              4

 9025               5

 7056               6

 5041               7

 3136               8

 1521               9

  400              10

 

So....11 values  of x  produce an  integer  output  for  y

 

cool cool cool

 

So      

 Aug 11, 2018

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