# 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
4 years, 1 month 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.......

- 4 years ago

*last

- 4 years ago

I believe the last problem has an issue.

- 4 years, 1 month ago

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

- 4 years, 1 month ago