837 Вправа 837Алгебра 8 клас Бевз 2025 · § 16 · стор. 157

837. Що більше: √2003 − √2001 чи √2004 − √2002?

${\displaystyle \sqrt{2003}-\sqrt{2001}=}$${\displaystyle \frac{2003-2001}{\sqrt{2003}+\sqrt{2001}}=}$${\displaystyle \frac{2}{\sqrt{2003}+\sqrt{2001}}}$;

${\displaystyle \sqrt{2004}-\sqrt{2002}=}$${\displaystyle \frac{2004-2002}{\sqrt{2004}+\sqrt{2002}}=}$${\displaystyle \frac{2}{\sqrt{2004}+\sqrt{2002}}}$;

${\displaystyle \sqrt{2003}+\sqrt{2001}<\sqrt{2004}+\sqrt{2002}}$, тому ${\displaystyle \sqrt{2003}-\sqrt{2001}>\sqrt{2004}-\sqrt{2002}}$.