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Algebra Level 3

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

10 11 6 7 9

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Rohit Udaiwal by Rohit Udaiwal , 20, India

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2 solutions

Akhil Bansal
Jan 5, 2016

120 − x \sqrt{120 - \sqrt{x}} will be an integer if
120 − x ∈ { 0 , 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 } 120 - \sqrt{x} \in \{ 0,1,4,9,16,25,36,49,64,81,100\}

Hence, 11 possible solutions.

8 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Great explanation. There is no need to figure out the exact value of x x .

If x will be 0 then √120 is not an integer.

Ramendra Polai - 5 years, 5 months ago

Instead of 56 it should be 64..Don't you think? @Akhil Bansal

Sagar Shah - 5 years, 5 months ago

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Thnx.. typo mistake

Akhil Bansal - 5 years, 4 months ago
Hasan Kibria
Jan 5, 2016

i think answer should be 10 cause 0 is not integer

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 is an integer. it is not a positive one.

Aareyan Manzoor - 5 years, 5 months ago

Integers include all negative numbers, all positive (natural) numbers, and 0.

Colin Carmody - 5 years, 5 months ago

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