Prove that in a Euclidean plane there are infinitely many concentric circles C such that all triangles inscribed in C have at least one irrational side.

inequality with a,b,c >0 and a + b + c = 1

Let a,b,c >0 and a + b + c = 1. Prove that: \frac{{2ab}}{{c + ab}} + \frac{{3bc}}{{a + bc}} + \frac{{2ca}}{{b + ca}} \ge \frac{5}{3}

$\left\{ \begin{array}{l}
\left( {x^2 + 1} \right)y^4 + 1 = 2xy^2 \left( {y^3 – 1} \right) \\
xy^2 \left( {3xy^4 – 2} \right) = xy^4 \left(…

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