Ответ:
1.x1 = 2, x2 = -2, x3 = -√2 х4 = √2
2.[tex]\frac{6(x-2,5)(x-\frac{1}{3} ) }{3(x-\frac{1}{3}) }[/tex]=[tex]\frac{6x-15}{3}[/tex]
3.
Объяснение:
x^4 - 6x^2 + 8 = 0
x^2 = y
y^2 - 6y + 8 = 0
D = (-6)^2 - 4(1 * 8) = 36 - 32 = 4
y1 = -(-6) - √4 / 2 * 1 = 6-2 / 2 = 4/2 = 2
y2 = -(-6)+√4/2*1 = 6+2/2 = 8/2 = 4
x^2 = y
x1 = √2
x2 = -√2
x3 = -2
x4 = 2
2. 6x^2+13x-5/3x-1
[tex]\left \{ {{6x^2+13x-5=0} \atop {3x-1\neq0}} \right.[/tex]
[tex]\left \{ {{6x^2+13x-5=0} \atop {x\neq \frac{1}{3} }} \right.[/tex]
[tex]6x^{2}[/tex]+13x-5=0
D=[tex]13^{2}[/tex]-4(6*(-5))=169+120=289=[tex]17^{2}[/tex]
[tex]x_{1}[/tex]=[tex]\frac{-13-\sqrt{289} }{2*6}[/tex]=[tex]\frac{-30}{12}[/tex]=-2,5
[tex]x_{2}[/tex]=[tex]\frac{-13+\sqrt{289} }{2*16}[/tex]=[tex]\frac{4}{12}[/tex]=[tex]\frac{1}{3}[/tex]
[tex]\frac{6(x-2,5)(x-\frac{1}{3} ) }{3(x-\frac{1}{3}) }[/tex]=[tex]\frac{6x-15}{3}[/tex](х-[tex]\frac{1}{3}[/tex] сокращается, и раскрываем скобки)