# Monthly maths problem: March 2020

Thursday 12th March 2020

Find a polynomial with integer coefficients which has as a root \(\sqrt{2}+\sqrt{3}\).

We could try: \[(x-\sqrt{2}-\sqrt{3}) (x+\sqrt{2}+\sqrt{3}) (x-\sqrt{2}+\sqrt{3}) (x+\sqrt{2}-\sqrt{3})\]

\[=(x^2+5+2\sqrt{6}) (x^2+5-2\sqrt{6})\]

\[(x^2+5)^2-24=x^4+10x^2+1\]

By **Chris Luke**