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Cool problems (Part 2)

This is the continue of Cool nt problems. These are some problems I've found on internet and I've really liked them.

  • Find all real solutions of this sistem:

\(\sqrt{x^{2}+y^{2}+6x+9}+ \sqrt{ x^{2}+y^{2}-8y+16} = 5\)

\(9y^{2}-4x^{2}= 60\)

  • Find all real solutions of \(x^{6}+y^{6}+z^{6}= 6xyz - 3\)

  • Let n be a positive integer. Show that \(N = 11111(2n times)2222(n times)\) is a perfect square.

Note by Jordi Bosch
3 years, 5 months ago

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The lat digit of the number given in the third problem is 2 right? So how can it be a perfect square.......

Eddie The Head - 3 years, 4 months ago

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*last

Eddie The Head - 3 years, 4 months ago

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I believe the last problem has an issue.

Bogdan Simeonov - 3 years, 5 months ago

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yes it must be 1111(2n times)2222(n times)

Jordi Bosch - 3 years, 5 months ago

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