Question

Sa se compare numerele

Answer 1

Explicație pas cu pas:

Observam ca 26-13 = 17 - 6 ,ceea ce ne duce cu gandul sa separam termenii.

$\sqrt{26} +\sqrt{6} ~~~~ \sqrt{13}+\sqrt{17}\\\sqrt{26}-\sqrt{13} ~~~~~ \sqrt{17}-\sqrt{6}$

Mai departe putem amplifica cu conjugatul.

$\dfrac{(\sqrt{26}-\sqrt{13})(\sqrt{26}+\sqrt{13})}{\sqrt{26}+\sqrt{13}}~~~~~ \dfrac{(\sqrt{17}+\sqrt 6)(\sqrt{17}-\sqrt 6)}{\sqrt{17}+\sqrt 6}\\\dfrac{26-13}{\sqrt{26}+\sqrt{13}}~~~~ \dfrac{17-6}{\sqrt{17}+\sqrt 6}\\\dfrac{13}{\sqrt{26}+\sqrt{13}} ~~~~~ \dfrac{13}{\sqrt{17}+\sqrt 6}|:13\\\dfrac{1}{\sqrt{26}+\sqrt{13}} ~~~~  \dfrac{1}{\sqrt{17}+\sqrt 6}\\\text{Evident, }\sqrt{26}+\sqrt{13} > \sqrt{17}+\sqrt 6,\text{ceea ce inseamna ca }\\\dfrac{1}{\sqrt{26}+\sqrt{13}}<\dfrac{1}{\sqrt{17}+\sqrt 6}$

Prin urmare, a < b .