Question

Cât face (3√2 - 2√3) : (2√3 - 3√2)?

Answer 1

   
[tex]\displaystyle\\ \Big(3\sqrt{2} - 2\sqrt{3}\Big) : \Big(2\sqrt{3} - 3\sqrt{2}\Big) = ?\\\\ \text{comparam numerele }~3\sqrt{2}~\text{ si }~2\sqrt{3}\\\\ \Big(3\sqrt{2}\Big)^2 = 9 \times 2 = 18\\ \Big(2\sqrt{3}\Big)^2 = 4 \times 3 = 12\\ \Longrightarrow~~3\sqrt{2} \ \textgreater \ 2\sqrt{3}\\\\ \Big(3\sqrt{2} - 2\sqrt{3}\Big) \ \textgreater \ 0~\text{ iar }~ \Big(2\sqrt{3} - 3\sqrt{2}\Big)\ \textless \ 0 \\\\ \Longrightarrow~~\Big(2\sqrt{3} - 3\sqrt{2}\Big)= -\Big(3\sqrt{2} - 2\sqrt{3}\Big) \\\\ [/tex]


[tex]\displaystyle\\ \Longrightarrow~\Big(3\sqrt{2} - 2\sqrt{3}\Big) : \Big(2\sqrt{3} - 3\sqrt{2}\Big) =\\\\ = \frac{3\sqrt{2} - 2\sqrt{3}}{2\sqrt{3} - 3\sqrt{2}}= \frac{3\sqrt{2} - 2\sqrt{3}}{-\Big(3\sqrt{2} - 2\sqrt{3}\Big)}=-\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} - 2\sqrt{3}}= \boxed{\bf -1}[/tex]