Question

7.Rezolvati urmatoarele ecuatii,unde x apartine R \ {0}.

a) 24:x=4 radical 3.
b) 20:x=2 radical 5
c) 45:x=5 radical 3
d) (-7 radical 10):x=7 radical 2

Answer 1

   
[tex]\displaystyle\\ a)\\ 24:x=4 \sqrt{3} \\\\ \frac{24}{x} =4\sqrt{3} \\\\ x=\frac{24}{4\sqrt{3}}= \frac{6}{\sqrt{3}}=\frac{6\sqrt{3}}{3}=\boxed{\bf 2\sqrt{3}}\\\\ b)\\ 20:x=2 \sqrt{5}\\\\ \frac{20}{x} =2\sqrt{5}\\\\ x=\frac{20}{2\sqrt{5}}=\frac{10}{\sqrt{5}}=\frac{10\sqrt{5}}{5}=\boxed{\bf 2\sqrt{5}}\\\\ c)\\ 45:x=5\sqrt{3}\\\\ \frac{45}{x}=5\sqrt{3}\\\\ x=\frac{45}{5\sqrt{3}}=\frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=\boxed{\bf3\sqrt{3}}[/tex]

[tex]\displaystyle d)\\ (-7\sqrt{10}):x=7\sqrt{2}\\\\ \frac{-7\sqrt{10}}{x}= 7\sqrt{2}\\\\ x=\frac{-7\sqrt{10}}{7\sqrt{2}}=\boxed{\bf -\sqrt{5}}[/tex]