Matematyka.pl

\(\displaystyle{ \sqrt{27-10\sqrt{2}}}\) + \(\displaystyle{ \sqrt{27+10\sqrt{2}}}\)

janko2, zauważ że:\(\displaystyle{ 27-10\sqrt{2}=(5-\sqrt{2})^2}\)

\(\displaystyle{ x=\sqrt{27-10\sqrt{2}}+\sqrt{27+10\sqrt{2}} \\ x^2=27-10\sqrt2+2\sqrt{27^2-(10\sqrt2)^2}+27+10\sqrt2 \\ x^2=54+2\sqrt{529} \\ x^2=100 \\x=10}\)

Matematyka.pl

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