a) [tex]\frac{x}{64}=\frac{625}{x}[/tex]
[tex]x^{2} =64\cdot \:625[/tex]
[tex]x^2=40000[/tex]
[tex]x=\sqrt{40000},\:x=-\sqrt{40000}[/tex]
[tex]x=\sqrt{40000} =\sqrt{200^2} =200[/tex]
[tex]x=-\sqrt{40000} =-\sqrt{200^2} =-200[/tex]
[tex]x=200,\:x=-200[/tex]
b) [tex]\frac{3.6}{x}=\frac{x}{12.1}[/tex]
[tex]3.6\cdot \:12.1=xx[/tex]
[tex]43.56=x^2[/tex]
[tex]x=\sqrt{43.56},\:x=-\sqrt{43.56}[/tex]
c) [tex]\frac{x}{6\sqrt{12}}=\frac{25\sqrt{27}}{x}[/tex]
[tex]\frac{\sqrt{3}x}{36}=\frac{75\sqrt{3}}{x}[/tex]
[tex]\sqrt{3}xx=36\cdot \:75\sqrt{3}[/tex]
[tex]\sqrt{3}x^2=2700\sqrt{3}[/tex]
[tex]x=-30\sqrt{3},\:x=30\sqrt{3}[/tex]
d) [tex]\frac{4\frac{1}{5}}{x}=\frac{x}{2\frac{1}{7}}[/tex]
[tex]\frac{\frac{21}{5}}{x}=\frac{x}{2\frac{1}{7}}[/tex]
[tex]\frac{\frac{21}{5}}{x}=\frac{x}{\frac{15}{7}}[/tex]
[tex]\frac{21}{5x}=\frac{7x}{15}[/tex]
[tex]21\cdot \:15=5x\cdot \:7x[/tex]
[tex]315=35x^2[/tex]
[tex]x=3,\:x=-3[/tex]
e. [tex]\frac{5x}{48}=\frac{80}{3x}[/tex]
[tex]5x\cdot \:3x=48\cdot \:80[/tex]
[tex]15x^2=3840[/tex]
[tex]x=16,\:x=-16[/tex]
f) [tex]\frac{x-6}{96}=\frac{24}{x-6}[/tex]
[tex]\left(x-6\right)\left(x-6\right)=96\cdot \:24[/tex]
[tex]\left(x-6\right)^2=2304[/tex]
[tex]x=54,\:x=-42[/tex]
Sper că te-am ajutat!
Succes!
#copăceibrainly
