Question

13 va rog dau coroana

Answer 1

Explicație pas cu pas:

Ca să compari x si y ridici la patrat radicalii

Answer 2

$\displaystyle Introducem~factorii~sub~radical:\\\\ a)~x=2\sqrt{3} ~si~y=3\sqrt{2} \\\\ \left\begin{array}{ccc}x=2\sqrt{3} =\sqrt{2^2 \cdot 3}=\sqrt{4 \cdot 3}=\sqrt{12}\\\\y=3\sqrt{2}=\sqrt{3^2 \cdot 2}=\sqrt{9 \cdot 2}=\sqrt{18} \end{array}\right| \Rightarrow 12 < 18 \Rightarrow x < y$

$\displaystyle b)~x=2\sqrt{7} ~si~y=3\sqrt{3} \\\\ \left\begin{array}{ccc}x=2\sqrt{7}=\sqrt{2^2\cdot7}=\sqrt{4 \cdot 7}=\sqrt{28} \\\\y=3\sqrt{3} =\sqrt{3^2\cdot3}=\sqrt{9 \cdot3}=\sqrt{27} \end{array}\right|\Rightarrow 28 > 27 \Rightarrow x > y$

$c)~x=4\sqrt{5} ~si~y=5\sqrt{3} \\\\ \left\begin{array}{ccc}x=4\sqrt{5} =\sqrt{4^2\cdot5}=\sqrt{16\cdot5}=\sqrt{80} \\\\ y=5\sqrt{3} =\sqrt{5^2 \cdot 3}=\sqrt{25 \cdot 3}= \sqrt{75} \end{array}\right|\Rightarrow 80 > 75 \Rightarrow x > y$

$d)~x=4\sqrt{3} ~si~y=5\sqrt{2}\\\\ \left\begin{array}{ccc}x=4\sqrt{3}=\sqrt{4^2 \cdot 3}=\sqrt{16 \cdot 3}=\sqrt{48}\\\\y=5\sqrt{2} =\sqrt{5^2\cdot2}=\sqrt{25 \cdot 2}=\sqrt{50}\end{array}\right| \Rightarrow 48 < 50 \Rightarrow x < y$