$a)$

$3x^4-9x^2=0$

$3x^2\left(x^2-3\right)=0$

$3x^2\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)=0$

$x=0\vee x=\sqrt{3}\vee x=-\sqrt{3}$

 

 

 

$b)$

$64x^5=-x^2\mid +x^2$

$64x^5+x^2=0$

$x^2\left(64x^3+1\right)=0$

$x^2\left({\left(4x\right)}^3+1^3\right)=0$

$x^2\left(4x+1\right)\stackrel{\Delta =16-4\cdot 16<0}{\left(16x^2+4x+1\right)}=0$

$x=0\vee 4x+1=0$

$x=-\frac{1}{4}$

 

 

 

$c)$

$\frac{1}{4}{x}^6=9x^2\mid \cdot 4$

$x^6=36x^2\mid -36x^2$

$x^6-36x^2=0$

$x^2\left(x^4-36\right)=0$

$x^2\left(x^2-36\right)\left(x^2+36\right)=0$

$x^2\left(x-6\right)\left(x+6\right)\stackrel{\Delta =0-4\cdot 36<0}{\left(x^2+36\right)}=0$

$x=0\vee x=6\vee x=-6$