1) Ta có: \(\left(3-x^2\right)+6-2x=0\)

\(\Leftrightarrow3-x^2+6-2x=0\)

\(\Leftrightarrow-x^2-2x+9=0\)

\(\Leftrightarrow x^2+2x-9=0\)

\(\Leftrightarrow x^2+2x+1=10\)

\(\Leftrightarrow\left(x+1\right)^2=10\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=\sqrt{10}\\x+1=-\sqrt{10}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{10}-1\\x=-\sqrt{10}-1\end{matrix}\right.\)

Vậy: \(S=\left\{\sqrt{10}-1;-\sqrt{10}-1\right\}\)

2) Ta có: \(5\left(2x-1\right)+7=4\left(2-x\right)+2\)

\(\Leftrightarrow10x-5+7=8-4x+2\)

\(\Leftrightarrow10x+4x=8+2+5-7\)

\(\Leftrightarrow14x=8\)

\(\Leftrightarrow x=\dfrac{4}{7}\)

Vậy: \(S=\left\{\dfrac{4}{7}\right\}\)

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

\(\Leftrightarrow x\left(x-6\right)+4\left(x-6\right)=0\)

\(\Leftrightarrow\left(x-6\right)\left(x+4\right)=0\)

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

Vậy: S={6;-4}

a) \(\left\{{}\begin{matrix}2x+3y=-5\\6x-5y=27\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}6x+9y=-15\\6x-5y=27\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}14y=-42\\2x+3y=-5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=-3\\2x+3.\left(-3\right)=-5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=-3\\2x-9=-5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=-3\\2x=4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=2\end{matrix}\right.\)

Vậy phương trình có nghiệm là: \(\left\{{}\begin{matrix}y=-3\\x=2\end{matrix}\right.\)

b) \(3x^2+4x=0\) 

\(\Leftrightarrow x\left(3x+4\right)=0\)

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

Vậy phương trình có tập nghiệm là: \(S=\left\{0;-\dfrac{4}{3}\right\}\)

c) Đặt:  \(x^2=t\left(t\ge0\right)\)

\(\Rightarrow\) Ta có phương trình mới:

\(t^2-3t-4=0\) 

Ta có: a - b + c = 1 + 3 - 4 = 0

\(\Rightarrow t_1=-1\left(loại\right);t_2=4\left(TM\right)\)

\(\Rightarrow x=\pm2\)

Vậy tập nghiệm của phương trình là: S = {2; -2}

a, \(\left\{{}\begin{matrix}2x+3y=-5\\6x-5y=27\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+9y=-15\left(1\right)\\6x-5y=27\left(2\right)\end{matrix}\right.\)

Lấy (1) - (2) ta được : \(14y=-15-27=-42\Leftrightarrow y=-3\)

\(\Rightarrow6x-27=-15\Leftrightarrow6x=12\Leftrightarrow x=2\)

Vậy \(\left(x;y\right)=\left(2;-3\right)\)

b, \(3x^2+4x=0\Leftrightarrow x\left(3x+4\right)=0\Leftrightarrow x=0;x=-\dfrac{4}{3}\)

c, \(x^4-3x^2-4=0\Leftrightarrow x^4+x^2-4x^2-4=0\)

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

\(\Leftrightarrow x=\pm2;x^2+1>0\)

Vậy nghiệm của phương trình là x = -2 ; x = 2 

Đặt \(x^2+6x+7=t\)

Bài toán trở thành tìm m để phương trình: \(\left(t-2\right)\left(t+1\right)=m-1\) (1) có nghiệm \(t< 0\)

\(\left(1\right)\Leftrightarrow t^2-t-1=m\)

Xét hàm \(f\left(t\right)=t^2-t-1\)

\(f\left(0\right)=-1\) và hàm số nghịch biến khi \(t< 0\)

\(\Rightarrow f\left(t\right)>-1\) \(\forall t< 0\)

\(\Rightarrow\) phương trình \(f\left(t\right)=m\) có nghiệm \(t< 0\) khi và chỉ khi \(m>-1\)

Vậy với \(m>-1\) thì pt đã cho có nghiệm thỏa \(x^2+6x+7< 0\)

a)\(3x^2-4x=0<=>x(3x-4)=0\)
TH1: x=0

TH2 3x-4=0 <=>x=4/3

KL:.....

b) .

<=> (x+3)(x-1+2x)=0

TH1: x+3=0 <=> x=-3

TH2  x-1=0  <=> x=1

KL:.....

c) \(9x^2+6x+1=0. <=>(3x+1)^2=0<=>3x+1=0<=>x=-1/3 ​\)

KL:......
d) \(x^2−4x=4.<=>(x-2)^2=0<=>x-2=0<=>x=2\)

KL:....

a) \(3x^2-4x=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{4}{3}\end{matrix}\right.\)

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

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

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

c) \(9x^2+6x+1=0\)

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

\(\Leftrightarrow3x+1=0\Leftrightarrow x=-\dfrac{1}{3}\)

d) \(x^2-4x=4\)

\(\Leftrightarrow\left(x-2\right)^2=8\)

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

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

\(2\left(2y^3+x^3\right)+3y\left(x+1\right)^2+6x\left(x+1\right)+2=0\)

\(\Leftrightarrow2\left(x^3+3x^2+3x+1\right)+3y\left(x+1\right)^2+4y^3=0\)

\(\Leftrightarrow2\left(x+1\right)^3+3\left(x+1\right)^2y+4y^3=0\)

Đặt \(x+1=a\)

\(\Rightarrow2a^3+3a^2y+4y^3=0\)

\(\Leftrightarrow\left(a+2y\right)\left(2a^2-ay+2y^2\right)=0\)

\(\Leftrightarrow\left(a+2y\right)\left(3a^2+3y^2+\left(a-y\right)^2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a+2y=0\\a=y=0\left(ktm\right)\end{matrix}\right.\)

\(\Leftrightarrow x+1+2y=0\Rightarrow x=-2y-1\)

Thế vào pt đầu:

\(\sqrt{\left(-2y-1\right)^2+2y+3}=3-2y\)

\(\Leftrightarrow\sqrt{4y^2+6y+4}=3-2y\) (\(y\le\dfrac{3}{2}\))

\(\Leftrightarrow18y=5\)

a. \(9\left(x+2\right)-3\left(x+2\right)=0\)

\(\Leftrightarrow9x+18-3x-6=0\)

\(\Leftrightarrow6x+12=0\)

\(\Leftrightarrow x=-2\)

e. \(\left(2x-1\right)^2-45=0\)

\(\Leftrightarrow4x^2-2x+1-45=0\)

\(\Leftrightarrow4x^2-2x-44=0\)

Đến đó tự giải tiếp nha!

c. \(2\left(2x-5\right)-3x=0\)

\(\Leftrightarrow4x-10-3x=0\)

\(\Leftrightarrow x-10=0\)

\(\Leftrightarrow x=10\)

g. \(2x^2-6x=0\)

\(\Leftrightarrow2x\left(x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)

b. Câu b bạn viết đề lại nhá!

d.\(\left(x-1\right)^2+x\left(5-x\right)=0\)

\(\Leftrightarrow x^2-2x+1+5x-x^2=0\)

\(\Leftrightarrow3x+1=0\)

\(\Leftrightarrow x=\dfrac{-1}{3}\)

e.

\(\left(2x-3\right)\left(2x+3\right)-\left(x+5\right)^2-3\left(x-1\right)\left(x+2\right)=0\)

\(\Leftrightarrow4x^2-9-x^2-10x-25-3x^2-3x+6=0\)

\(\Leftrightarrow-13x-28=0\)

\(\Leftrightarrow x=\dfrac{-28}{13}\)

a. \(x^2-7x+6=0\)

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

\(\Leftrightarrow\left(x^2-6x\right)-\left(x-6\right)=0\)

\(\Leftrightarrow x\left(x-6\right)-\left(x-6\right)=0\)

\(\Leftrightarrow\left(x-6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=6\end{matrix}\right.\)

a) Ta có: \(2x^3+5x^2-3x=0\)

\(\Leftrightarrow x\left(2x^2+5x-3\right)=0\)

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

\(\Leftrightarrow x\left[2x\left(x+3\right)-\left(x+3\right)\right]=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\2x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=\dfrac{1}{2}\end{matrix}\right.\)

Vậy: \(S=\left\{0;-3;\dfrac{1}{2}\right\}\)

b) Ta có: \(2x^3+6x^2=x^2+3x\)

\(\Leftrightarrow2x^2\left(x+3\right)=x\left(x+3\right)\)

\(\Leftrightarrow2x^2\left(x+3\right)-x\left(x+3\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\2x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\2x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=\dfrac{1}{2}\end{matrix}\right.\)

Vậy: \(S=\left\{0;-3;\dfrac{1}{2}\right\}\)

c) Ta có: \(x^2+\left(x+2\right)\left(11x-7\right)=4\)

\(\Leftrightarrow x^2+11x^2-7x+22x-14-4=0\)

\(\Leftrightarrow12x^2+15x-18=0\)

\(\Leftrightarrow12x^2+24x-9x-18=0\)

\(\Leftrightarrow12x\left(x+2\right)-9\left(x+2\right)=0\)

\(\Leftrightarrow\left(x+2\right)\left(12x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\12x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\12x=9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{3}{4}\end{matrix}\right.\)

Vậy: \(S=\left\{-2;\dfrac{3}{4}\right\}\)

Trong đó có nhiều phương trình kiến thức cơ bản mà nhỉ? Ít nâng cao, bạn lọc ra câu nào k làm đc thôi chứ!

1: \(\Leftrightarrow2x^2-10x-3x-2x^2=0\)

=>-13x=0

=>x=0

2: \(\Leftrightarrow5x-2x^2+2x^2-2x=13\)

=>3x=13

=>x=13/3

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

=>-2x^2=0

=>x=0

4: \(\Leftrightarrow5x^2-5x-5x^2+7x-10x+14=6\)

=>-8x=6-14=-8

=>x=1

`1)2x(x-5)-(3x+2x^2)=0`

`<=>2x^2-10x-3x-2x^2=0`

`<=>-13x=0`

`<=>x=0`

___________________________________________________

`2)x(5-2x)+2x(x-1)=13`

`<=>5x-2x^2+2x^2-2x=13`

`<=>3x=13<=>x=13/3`

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`3)2x^3(2x-3)-x^2(4x^2-6x+2)=0`

`<=>4x^4-6x^3-4x^4+6x^3-2x^2=0`

`<=>x=0`

___________________________________________________

`4)5x(x-1)-(x+2)(5x-7)=0`

`<=>5x^2-5x-5x^2+7x-10x+14=0`

`<=>-8x=-14`

`<=>x=7/4`

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`5)6x^2-(2x-3)(3x+2)=1`

`<=>6x^2-6x^2-4x+9x+6=1`

`<=>5x=-5<=>x=-1`

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`6)2x(1-x)+5=9-2x^2`

`<=>2x-2x^2+5=9-2x^2`

`<=>2x=4<=>x=2`

giúp em với mọi người ơi:<<<<<

câu a 

Gọi x₀ là nghiệm chung của PT(1) và (2)

\(\Rightarrow\left\{{}\begin{matrix}2x^2_0+\left(3m-1\right)x_0-3=0\left(\times3\right)\\6.x^2_0-\left(2m-1\right)x_0-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x^2_0+3\left(3m-1\right)x_0-9=0\left(1\right)\\6x^2_0-\left(2m-1\right)x_0-1=0\left(2\right)\end{matrix}\right.\)  Lấy (1)-(2) ,ta được 

PT\(\Leftrightarrow3\left(3m-1\right)-9+\left(2m-1\right)+1\)=0

     \(\Leftrightarrow9m-3-9+2m-1+1=0\Leftrightarrow11m-12=0\)

      \(\Leftrightarrow m=\dfrac{12}{11}\)