[latex]b)\\(x+1)^2(2x-4)=0\\x+1=0 vee 2x-4=0\\x=-1 vee 2x=4 /:2 \\x=-1 vee x=2[/latex] [latex]c)\\(5-x)(x^2-7x+10)=0 \\ 5-x=0 vee x^2-7x+10 =0 \\ x=5 vee Delta =b^2-4ac=(-7)^2-4*1*10=49-40=9\\sqrt{Delta }=sqrt{9}=3\\x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{ 7-3}{2 }=frac{4}{2}=2\\x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{ 7+3}{2 }=frac{10}{2}=5\\rozwiazaniem tego rownania jest:\x=2 vee x=5[/latex] [latex]d)\\(x^2+2x-3)(x-1)^3=0 \\ x^2+2x-3 =0 vee (x-1)=0\\ Delta =b^2-4ac = 2^2 -4*1* (-3)= 4+12=16 \ \sqrt{Delta }=sqrt{16}=4 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{-2-4}{2 }=frac{-6}{2}=-3\\x_{2}=frac{-b+sqrt{Delta } }{2a}=frac{-2+4}{2 }=frac{2}{2}=1\\ lub\\x-1=0\x=1\\rozwiazaniem tego rownania jest:\\x=-3 vee x=1[/latex] [latex]e)\\(x^2-9)(x+3)^2=0 \\x^2-9=0 vee x+3=0 \\(x-3)(x+3)=0 vee x=3\\x-3=0 vee x+3 =0 vee x=3\\x=3 vee x=-3 vee x=3\\rozwiazaniem tego rownania jest:\\x=-3 vee x=3[/latex] [latex]f)\\(x^2-x-6)(x^2+x-1)=0\\x^2-x-6=0\\ Delta =b^2-4ac = (-1)^2 -4*1* (-6)= 1+24=25 \ \sqrt{Delta }=sqrt{25}=5 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{1-5}{2 }=frac{-4}{2}= -2\\x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{1+5}{2 }=frac{6}{2}=3 [/latex] [latex]lub\\x^2+x-1 =0 \\ Delta =b^2-4ac = 1^2 -4*1* (-1)=1+4=5 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{-1-sqrt{5}}{2 } \\x_{2}=frac{-b+sqrt{Delta } }{2a}=frac{-1+sqrt{5}}{2 } \\ rozwiazaniem tego rownania jest:\\x=-2 vee x=frac{-1-sqrt{5}}{2 } vee x=frac{-1+sqrt{5}}{2 } vee x=3[/latex] [latex]g)\\(x^2-4)^2(x^4+3x^3-10x^2)=0\\x^2-4=0\\(x-2)(x+2)=0\\x-2=0 vee x+2=0\\x=2 vee x=-2[/latex] [latex]lub\\x^4+3x^3-10x^2 =0\\x^2 (x^2+3x -10)=0\\x=0 vee Delta =b^2-4ac =3^2 -4*1* (- 10)= 9+40=49 \ \sqrt{Delta }=sqrt{49}=7 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{ -3-7}{2 }=frac{-10}{2}=-5\ \x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{ -3+7}{2 }=frac{4}{2}=2\\ rozwiazaniem tego rownania jest:\\x=-5 vee x=-2 vee x=2 vee x=0[/latex]
