[tex]x^5-x^4-8x^3+8x^2+15x-15=0\\x^5-8x^3+15x-x^4+8x^2-15=0\\x(x^4-8x^2+15)-(x^4-8x^2+15)=0\\(x-1)(x^4-8x^2+15)=0\\x=1~\vee~x=\sqrt{3}~\vee~x=-\sqrt{3} ~\vee~x=\sqrt{5}~\vee~-\sqrt{5}[/tex]
[tex]x^4-8x^2+15=0,~~t=x^2~\land~t\geq 0\\t^2-8t+15=0\\\Delta=64-4(15)=4\\\sqrt{\Delta} =2\\t_1=\frac{8-2}{2}=3> 0\\t_2=\frac{8+2}{2}=5 > 0\\\\t=3~\vee~t=5\\x^2=3~\vee~x^2=5\\x=\sqrt{3}~\vee~x=-\sqrt{3} ~\vee~x=\sqrt{5}~\vee~-\sqrt{5}[/tex]
