f)
x^2=\sqrt2x^5
x^2-\sqrt2x^5=0
-x^2(\sqrt2x^3-1)=0
-x^2=0=> x=0
lub
\sqrt2x^3-1=0
\sqrt2x^3=1
x^3=\frac{1}{\sqrt2}
x^3=\frac{1}{2^{\frac{1}{2}}}/^{\frac{1}{3}}
x=\frac{1}{2^{\frac{1}{6}}}
x=\frac{1}{\sqrt[6]{2}}
x=\frac{1 * \sqrt[6]{32}}{\sqrt[6]{2} * \sqrt[6]{32}}
x=\frac{\sqrt[6]{32}}{\sqrt[6]{64}}
x=\frac{\sqrt[6]{32}}{2}
g)
6x^4-12x^3+6x^2=0
6x^2(x^2-2x+1)=0
6x^2(x-1)^2=0
6x^2=0\vee x-1=0
x_1=0 , x_2=1
h)
x^7-x^6=6x^5
x^7-x^6-6x^5=0
x^5(x^2-x-6)=0
x^5=0\vee x^2-x-6=0
x=0
lub
x^2-x-6=0
a=1, b=-1, c=-6
\Delta=1-4*(-6)=25
\sqrt\Delta=5
x_1=\frac{1-5}{2}=-2
x_2=\frac{1+5}{2}=3}
x_3=0
i)
\frac{1}{9}x^6+x^5=\frac{1}{3}x^5-x^4/*9
x^6+9x^5=3x^5-9x^4
x^6+9x^5-3x^5+9x^4=0
x^6+6x^5+9x^4=0
x^4(x^2+6x+9)=0
x^4(x+3)^2=0
x^4=0\vee x+3=0
x_1=0 , x_2=-3