Question

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Answer 1

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Answer 2

$\displaystyle a)~5x^2=320 \Rightarrow x^2=\frac{320}{5} \Rightarrow x^2=64 \Rightarrow x=\pm \sqrt{64} \Rightarrow x=\pm 8\\\\ b)~\frac{4}{3} \cdot x^2=\frac{16}{27}\Rightarrow 4x^2 \cdot 27=16 \cdot 3 \Rightarrow 108x^2=48 \Rightarrow x^2=\frac{48}{108}\Rightarrow \\\\ \Rightarrow x^2= \frac{4}{9} \Rightarrow x=\pm \sqrt{\frac{4}{9} } \Rightarrow x=\pm \frac{\sqrt{4} }{\sqrt{9} }\Rightarrow x=\pm\frac{2}{3}$

$\displaystyle c)~(x-1)^2=2,(7) \Rightarrow x^2-2 \cdot x \cdot 1+1^2=\frac{27-2}{9} \Rightarrow x^2-2x+1=\frac{25}{9} \Rightarrow \\\\ \Rightarrow9x^2-18x+9-25=0 \Rightarrow 9x^2-18x-16 =0 \\\\ \Delta=(-18)^2-4 \cdot 9 \cdot (-16)=324+576=900 > 0 \\\\x_1=\frac{-(-18)-\sqrt{900} }{2 \cdot 9}=\frac{18-30}{18}=\frac{-12}{18}=-\frac{2}{3} \\\\ x_2=\frac{-(-18)+\sqrt{900} }{2 \cdot 9}=\frac{18+30}{18}=\frac{48}{18}=\frac{8}{3}$

$\displaystyle d)~\frac{x}{20} =\frac{45}{x} \Rightarrow x \cdot x=45 \cdot 20 \Rightarrow x^2=900 \Rightarrow x=\pm\sqrt{900}\Rightarrow x=\pm30$

$\displaystyle e)~\frac{21}{8x} =\frac{3x}{14} \Rightarrow 21 \cdot 14=3x \cdot 8x \Rightarrow 294 =24x^2 \Rightarrow x^2=\frac{294}{24} \Rightarrow \\\\ \Rightarrow x^2=\frac{49}{4} \Rightarrow x=\pm \sqrt{\frac{49}{4} } \Rightarrow x=\pm \frac{\sqrt{49} }{\sqrt{4} }\Rightarrow x=\pm \frac{7}{2}$

$\displaystyle f)~\frac{2m-1}{3} =\frac{27}{2m-1} \Rightarrow (2m-1)(2m-1)=27 \cdot 3 \Rightarrow (2m-1)^2=81\Rightarrow \\\\ \Rightarrow (2m)^2-2\cdot 2m \cdot 1+1^2-81=0 \Rightarrow 4m^2-4m-80=0 \Big|:4 \Rightarrow \\\\ \Rightarrow m^2-m-20=0\\\\ \Delta=(-1)^2-4 \cdot 1 \cdot(-20)=1+80=81 > 0\\\\ x_1=\frac{-(-1)-\sqrt{81} }{2\cdot 1}=\frac{1-9}{2}=\frac{-8}{2}=-4\\\\x_2=\frac{-(-1)+\sqrt{81} }{2\cdot 1}=\frac{1+9}{2}=\frac{10}{2}=5$