Объяснение:

1.x=14

3.x1=-2,x2=-1,x3=1

4.x=-4

5. x^4-2x^3+x-30

Пояснення:

3.

Відповідь: [tex]x^3+2x^2-x-2=0\\\\x^2*(x+2)-(x+2)=0\\\\(x+2)*(x^2-1)=0\\\\(x+2)*(x+1)*(x-1)=0\\\\x_1=-2\ \ \ \ x_2=-1\ \ \ x_3=1.[/tex]

4.

[tex]\displaystyle\\(\frac{2x+1}{x-3}) ^2-3*\frac{2x+1}{x-3} +2=0\ \ \ \ \ \ x\neq 3.[/tex]

Нехай:

[tex]\displaystyle\\\frac{2x+1}{x-3} =t\ \ \ \ \Rightarrow\\\\t^2-3t+2=0\\\\t^2-2t-t+2=0\\\\t*(t-2)-(t-2)=0\\\\(t-2)*(t-1)=0\\\\t_1=\frac{2x+1}{x-3} =2\\\\2x+1=2*(x-3)\\\\2x+1=2x-6\\\\1\neq -6\ \ \ \ \Rightarrow\\\\x\in \varnothing.\\\\t_2=\frac{2x+1}{x-3} =1\\\\2x+1=1*(x-3)\\\\2x+1=x-3\\\\x=-4.[/tex]

Відповідь: х=-4.

5.

[tex]\displaystyle\\(x^2-x-1)*(x^2-x)-30=0[/tex]

Нехай:

[tex]\displaystyle\\x^2-x=t\ \ \ \ \ \ \Rightarrow\\\\(t-1)*t-30=0\\\\t^2-t-30=0\\\\t^2-6t+5t-30=0\\\\t*(t-6)+5*(t-6)=0\\\\(t-6)*(t+5)=0\\\\t_1=x^2-x=6\\\\x^2-x-6=0\\\\x^2-3x+2x-6=0\\\\x*(x-3)+2*(x-3)=0\\\\(x-3)*(x+2)=0\\\\x_1=3\ \ \ \ x_2=-2.\\\\t_2=x^2-x=-5\\\\x^2-x+5=0\\\\D=-19\ \ \ \ \ \ \Rightarrow\\\\x\in \varnothing.[/tex]

Відповідь: х₁=3    х₂=-2.