Question

Compara numerele: a=√99+√101 si b=√98+√102

Answer 1

[tex]a\ ?\ b\\ \sqrt{99}+\sqrt{101}\ \ \sqrt{98}+\sqrt{102}\\ \sqrt{99}-\sqrt{98}\ \ \sqrt{102}-\sqrt{101}\\ \text{Daca rationalizam cele doua fractii obtinem:}\\ \dfrac{99-98}{\sqrt{99}+\sqrt{98}}\ \ \dfrac{102-101}{\sqrt{102}+\sqrt{101}}\\ \dfrac{1}{\sqrt{99}+\sqrt{98}}\ \ \dfrac{1}{\sqrt{102}+\sqrt{101}}\\ \text{Deoarece } \sqrt{99}+\sqrt{98} \ \textless \ \sqrt{102}+\sqrt{101}\Rightarrow \dfrac{1}{\sqrt{99}+\sqrt{98}} \ \textgreater \ \dfrac{1}{\sqrt{102}+\sqrt{101}}\\ \text{Deci}\ a\ \textgreater \ b [/tex]