[latex]1)\3(x+5)(x-7)(4x-9)=0 /:3\(x+5)(x-7)(4x-9)=0\x+5=0 vee x-7=0 vee 4x-9=0\x=-5 x=7 x=2 frac{1}{4}[/latex] [latex]2)\4x^5-4x^4+x^3=0\x^3(4x^2-4x+1)=0\x^3(2x-1)^2=0\x^3=0 vee 2x-1=0\x=0 x=frac{1}{2}[/latex] [latex]3)\x^3-5x^2-2x+10=0\x^2(x-5)-2(x-5)=0\(x-5)(x^2-2)=0\(x-5)(x-sqrt2)(x+sqrt2)=0\x=5 vee x=sqrt2 vee x=-sqrt2[/latex] [latex]4)\x^3-3x^2=4x-12\x^3-3x^2-4x+12=0\x^2(x-3)-4(x-3)=0\(x-3)(x^2-4)=0\(x-3)(x-2)(x+2)=0\x=3 vee x=2 vee x=-2[/latex] [latex]5)\5x^3-15x^2-x+3 > 0\5x^2(x-3)-(x-3) >0\(x-3)(5x^2-1) >0\(x-3)(sqrt5x-1)(sqrt5x+1)>0\pierwiastki:\x=3 vee x=frac{sqrt5}{5} vee x=-frac{sqrt5}{5}\ odp:\ x in (-frac{sqrt5}{5},frac{sqrt5}{5}}) vee (3,+infty)[/latex] [latex]6)\(x+2)(x-1)(x+4) leq 0\pierwiastki:\x=-2 vee x=1 vee x=-4\\odp: xin(-infty,-4> vee <-2,1>[/latex] [latex]7)\(2x-1)(2x+1)(x-4) geq 0\pierwiastki:\x=frac{1}{2} vee x=-frac{1}{2} vee x=4\\odp:\xin<-frac{1}{2},frac{1}{2}> vee <4,+infty)[/latex]
