\(x^3-x^2-2x=0\)

⇔ \(x^3-2x^2+x^2-2x=0\)

⇔ \(x^2\left(x-2\right)+x\left(x-2\right)\) = 0

⇔\(\left(x-2\right)\left(x^2-x\right)=0\)

⇔ \(x\left(x-2\right)\left(x+1\right)\) = 0

⇔ \(\left[{}\begin{matrix}x=0\\x-2=0\\x+1=0\end{matrix}\right.\)

⇔\(\left[{}\begin{matrix}x=0\\x=2\\x=-1\end{matrix}\right.\)

Vậy phương trình có tập nghiệm S = \(\left\{0,2,-1\right\}\)

\(\Leftrightarrow\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^2-4x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2-4x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2-\sqrt{3}\\x=2+\sqrt{3}\end{matrix}\right.\)

Ta có: \(x^3-3x^2-3x+1=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x^2-4x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\sqrt{3}+2\\x=-\sqrt{3}+2\end{matrix}\right.\)

1, \(\Delta=\left(-11\right)^2-4.1.38=121-152=-31< 0\)

\(\Rightarrow\) pt vô nghiệm

2, \(\Delta=71^2-4.6.175=5041-4200=841\)

\(x_1=\dfrac{-71+\sqrt{841}}{2.6}=\dfrac{-71+29}{12}=\dfrac{-42}{12}=-\dfrac{7}{2}\)

\(x_2=\dfrac{-71-\sqrt{841}}{2.6}=\dfrac{-71-29}{12}=\dfrac{-10}{12}=-\dfrac{25}{3}\)

3, \(\Delta=\left(-3\right)^2-5.27=9-135=-126< 0\)

⇒ pt vô nghiệm

4, \(\Delta=15^2-\left(-30\right)\left(-7,5\right)=225-225=0\)

\(\Rightarrow x_1=x_2=\dfrac{-30}{2.\left(-30\right)}=\dfrac{1}{2}\)

5, \(\Delta'=\left(-8\right)^2-4.17=64-68=-4\)

⇒ pt vô nghiệm

6, \(\Delta=4^2-4.1.\left(-12\right)=16+48=64\)

\(x_1=\dfrac{-4+\sqrt{64}}{2.1}=\dfrac{-4+8}{2}=\dfrac{4}{2}=2\)

​\(x_2=\dfrac{-4-\sqrt{64}}{2.1}=\dfrac{-4-8}{2}=\dfrac{-12}{2}=-6\)​

mk làm rồi đó bạn xem đi Xem câu hỏi

a: \(\Leftrightarrow\left(-x+3\right)\left(x+6\right)=18\)

\(\Leftrightarrow-x^2-6x+3x+18-18=0\)

\(\Leftrightarrow-x\left(x+3\right)=0\)

=>x=0 hoặc x=-3

b: \(\Leftrightarrow x\left(3x^2+6x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\3x^2+6x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x^2+2x-\dfrac{4}{3}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x+1\right)^2=\dfrac{7}{3}\end{matrix}\right.\Leftrightarrow x\in\left\{0;\dfrac{\sqrt{21}}{3}-1;\dfrac{-\sqrt{21}}{3}-1\right\}\)

c: =>x(3x-5)=0

=>x=0 hoặc x=5/3

d: =>(x-2)(x+2)=0

=>x=2 hoặc x=-2

\(4x^4-11x^2+6=0\)

\(\Leftrightarrow4x^4-8x^2-3x^2+6=0\)

\(\Leftrightarrow4x^2\left(x^2-2\right)-3\left(x^2-2\right)=0\)

\(\Leftrightarrow\left(x^2-2\right)\left(4x^2-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2-2=0\\4x^2-3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\pm\sqrt{2}\\x=\pm\sqrt{\frac{3}{4}}\end{cases}}\)

\(S=\left\{\pm\sqrt{2};\pm\sqrt{\frac{3}{4}}\right\}\)

nếu có sai  bn thông cảm nha

Đặt \(a=x^2\)

\(\Rightarrow4a^2-11a+6=0\)

ta có: \(\Delta=11^2-4.4.6=121-96=25>0\)

=> Phương trình có 2 nghiệm phân biệt: \(a1=\frac{-b+\sqrt{\Delta}}{2a}=\frac{11+\sqrt{25}}{2.4}=\frac{16}{8}=2\Leftrightarrow x^2=2\Leftrightarrow x=\pm\sqrt{2}\)

                                                                 \(a2=\frac{-b-\sqrt{\Delta}}{2a}=\frac{11-\sqrt{25}}{2.4}=\frac{6}{8}=\frac{3}{4}\)\(\Leftrightarrow x^2=\frac{3}{4}\Leftrightarrow x=\pm\sqrt{\frac{3}{4}}\)

\(\frac{3}{5}-\sqrt{16}+\sqrt{0,16}+\sqrt{\frac{3}{52}}-\sqrt{\left(-5,5\right)^2}\)