$\text{a)}8x^5=2x^3$  

$8x^5-2x^3=0\mid :8$  

$x^5-\frac{1}{4}{x}^3=0$  

$x^3\left(x^2-\frac{1}{4}\right)=0$  

$x^3=0\text{lub}{x}^2-\frac{1}{4}=0$  

$x=0\text{lub}{x}^2=\frac{1}{4}$  

$x=0\text{lub}x=\frac{1}{2}\text{lub}x=-\frac{1}{2}$  

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$\text{b)}{x}^5=9x$  

$x^5-9x=0$  

$x\left(x^4-9\right)=0$  

$x=0\text{lub}{x}^4-9=0$  

$x=0\text{lub}{x}^4=9$  

$x=0\text{lub}{x}^4={\left(\sqrt{3}\right)}^4$  

$x=0\text{lub}x=\sqrt{3}\text{lub}x=-\sqrt{3}$  

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$\text{c)}0,375x^5=3x^2$  

$0,375x^5-3x^2=0$  

$\frac{3}{8}{x}^5-3x^2=0\mid \cdot \frac{8}{3}$  

$x^5-8x^2=0$  

$x^2\left(x^3-8\right)=0$  

$x^2=0\text{lub}{x}^3-8=0$  

$x=0\text{lub}{x}^3=8$  

$x=0\text{lub}x=2$  

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$\text{d)}{x}^3-6x=5x^2$  

$x^3-5x^2-6x=0$  

$x\left(x^2-5x-6\right)=0$  

$x=0\text{lub}\underset{\Delta =25+24=49,\sqrt{\Delta }=7}{x^2-5x-6=0}$  

$x=0\text{lub}x=\frac{5-7}{2}=\frac{-2}{2}=-1\text{lub}x=\frac{5+7}{2}=\frac{12}{2}=6$  

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$\text{e)}{x}^4+6x^2=8x^3$  

$x^4-8x^3+6x^2=0$  

$x^2\left(x^2-8x+6\right)=0$  

$x^2=0\text{lub}\underset{\Delta =64-24=40,\sqrt{\Delta }=2\sqrt{10}}{x^2-8x+6=0}$  

$x=0\text{lub}x=\frac{8-2\sqrt{10}}{2}=4-\sqrt{10}\text{lub}x=\frac{8+2\sqrt{10}}{2}=4+\sqrt{10}$  

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$\text{f)}{x}^4+4x^2=5x^3$  

$x^4-5x^3+4x^2=0$  

$x^2\left(x^2-5x+4\right)=0$  

$x^2=0\text{lub}\underset{\Delta =25-16=9,\sqrt{\Delta }=3}{x^2-5x+4=0}$  

$x=0\text{lub}x=\frac{5-3}{2}=\frac{2}{2}=1\text{lub}x=\frac{5+3}{2}=\frac{8}{2}=4$