b, x = -5/3 hoặc x = 4/3.

c, x = 0 hoặc x = 3, -3.

d, x = 0 hoặc x = 2, -2.

e, x = 1 hoặc x = \(\dfrac{-1}{2}\).

a: \(\Leftrightarrow x^2-40x+400-x^2-4x-3=-7\)

=>-44x+397=-7

=>-44x=-404

hay x=101

b: \(\Leftrightarrow\left[{}\begin{matrix}3x+5=0\\4-3x=0\end{matrix}\right.\Leftrightarrow x\in\left\{-\dfrac{5}{3};\dfrac{4}{3}\right\}\)

c: \(\Leftrightarrow x\left(x^2-9\right)=0\)

=>x(x-3)(x+3)=0

hay \(x\in\left\{0;3;-3\right\}\)

d: \(\Leftrightarrow x\left(x-2\right)\left(x+2\right)=0\)

hay \(x\in\left\{0;2;-2\right\}\)

e: =>(2x+1)(1-x)=0

=>x=-1/2 hoặc x=1

a) \(\left(3x-1\right)\left(2x+7\right)-\left(x+1\right)\left(6x-5\right)=16\)

\(\Leftrightarrow\left(6x^2+21x-2x-7\right)-\left(6x^2-5x+6x-5\right)-16=0\)

\(\Leftrightarrow6x^2+21x-2x-7-6x^2+5x-6x+5-16=0\)

\(\Leftrightarrow18x-18=0\)

\(\Leftrightarrow18x=18\)

\(\Leftrightarrow x=18:18\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

b) \(\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-5\right)+\left(2x-5\right)^2=x^2+6x+64\)

\(\Leftrightarrow\left[\left(2x+3\right)-\left(2x-5\right)\right]^2-\left(x^2+6x+64\right)=0\)

\(\Leftrightarrow\left(2x+3-2x+5\right)^2-x^2-6x-64=0\)

\(\Leftrightarrow8^2-x^2-6x-64=0\)

\(\Leftrightarrow64-x^2-6x-64=0\)

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

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

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

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

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

Vậy \(x=0\) hoặc \(x=-6\)

a) \(\left(3x-1\right)\left(2x+7\right)-\left(x+1\right)\left(6x-5\right)=16\)

\(\Leftrightarrow\left(6x^2+21x-2x-7\right)-\left(6x^2-5x+6x-5\right)-16=0\)

\(\Leftrightarrow6x^2+21x-2x-7-6x^2+5x-6x+5-16=0\)

\(\Leftrightarrow18x-18=0\)

\(\Leftrightarrow18x=18\)

\(\Leftrightarrow x=18:18\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

b, \(\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-5\right)+\left(2x- 5\right)^2=x^2+6x+64\)

\(\Leftrightarrow\left[\left(2x+3\right)-\left(2x-5\right)\right]^2- \left(x^2+6x+64\right)=0\)

\(\Leftrightarrow\left(2x+3-2x+5\right)^2-x^2-6x-64=0\)

\(\Leftrightarrow8^2-x^2-6x-64=0\)

\(\Leftrightarrow64-x^2-6x-64=0\)

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

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

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

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

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

Vậy \(x=0\) hoặc \(x=6\)

a) (3x−1)(2x+7)−(x+1)(6x−5)=16(3x−1)(2x+7)−(x+1)(6x−5)=16

⇔(6x2+21x−2x−7)−(6x2−5x+6x−5)−16=0⇔(6x2+21x−2x−7)−(6x2−5x+6x−5)−16=0

⇔6x2+21x−2x−7−6x2+5x−6x+5−16=0⇔6x2+21x−2x−7−6x2+5x−6x+5−16=0

⇔18x−18=0⇔18x−18=0

⇔18x=18⇔18x=18

⇔x=18:18⇔x=18:18

⇔x=1⇔x=1

Vậy x=1x=1

b) (2x+3)2−2(2x+3)(2x−5)+(2x−5)2=x2+6x+64(2x+3)2−2(2x+3)(2x−5)+(2x−5)2=x2+6x+64

⇔[(2x+3)−(2x−5)]2−(x2+6x+64)=0⇔[(2x+3)−(2x−5)]2−(x2+6x+64)=0

⇔(2x+3−2x+5)2−x2−6x−64=0⇔(2x+3−2x+5)2−x2−6x−64=0

⇔82−x2−6x−64=0⇔82−x2−6x−64=0

⇔64−x2−6x−64=0⇔64−x2−6x−64=0

⇔−x2−6x=0⇔−x2−6x=0

⇔x(−x−6)=0⇔x(−x−6)=0

⇔[x=0−x−6=0⇔[x=0−x−6=0

⇔[x=0−x=6⇔[x=0−x=6

⇔[x=0x=−6⇔[x=0x=−6

Vậy x=0x=0 hoặc x=−6

giúp mình bài ni với :3x^2(x+1)-5x(x+1)^2+4(x+1)

Giải:

1) \(\left(x-6\right)\left(x^2+6x+36\right)-\left(x+4\right)^3=\left(x-2\right)^3+\left(x+5\right)\left(x^2-10x+25\right)-\left(2x^3+6x^2\right)\)

\(\Leftrightarrow x^3-216-\left(x^3+12x^2+48x+64\right)=x^3-6x^2+12x-8+x^3+125-2x^3-6x^2\)

\(\Leftrightarrow x^3-216-x^3-12x^2-48x-64=x^3-6x^2+12x-8+x^3+125-2x^3-6x^2\)

\(\Leftrightarrow-280-12x^2-48x=-12x^2+12x+117\)

\(\Leftrightarrow-280-48x-12x-117=0\)

\(\Leftrightarrow-397-60x=0\)

\(\Leftrightarrow-60x=397\)

\(\Leftrightarrow x=-\dfrac{397}{60}\)

Vậy ...

2) \(\left(2x+3\right)^3-\left(2x+5\right)\left(4x^2-10x+25\right)=\left(6x-1\right)^2-\left(x-2\right)\left(x^2+2x+4\right)+x^3\)

\(\Leftrightarrow8x^3+36x^2+54x+27-\left(8x^3+125\right)=36x^2-12x+1-\left(x^3-8\right)+x^3\)

\(\Leftrightarrow8x^3+36x^2+54x+27-8x^3-125=36x^2-12x+1-x^3+8+x^3\)

\(\Leftrightarrow54x-98=-12x+9\)

\(\Leftrightarrow54x+12x=9+98\)

\(\Leftrightarrow66x=107\)

\(\Leftrightarrow x=\dfrac{107}{66}\)

Vậy ...

a) \(\sqrt[]{x^2-4x+4}=x+3\)

\(\Leftrightarrow\sqrt[]{\left(x-2\right)^2}=x+3\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-\left(x+3\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}0x=5\left(loại\right)\\x-2=-x-3\end{matrix}\right.\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

b) \(2x^2-\sqrt[]{9x^2-6x+1}=5\)

\(\Leftrightarrow2x^2-\sqrt[]{\left(3x-1\right)^2}=5\)

\(\Leftrightarrow2x^2-\left|3x-1\right|=5\)

\(\Leftrightarrow\left|3x-1\right|=2x^2-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2x^2-5\\3x-1=-2x^2+5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-4=0\left(1\right)\\2x^2+3x-6=0\left(2\right)\end{matrix}\right.\)

Giải pt (1)

\(\Delta=9+32=41>0\)

Pt \(\left(1\right)\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt[]{41}}{4}\)

Giải pt (2)

\(\Delta=9+48=57>0\)

Pt \(\left(2\right)\) \(\Leftrightarrow x=\dfrac{-3\pm\sqrt[]{57}}{4}\)

Vậy nghiệm pt là \(\left[{}\begin{matrix}x=\dfrac{3\pm\sqrt[]{41}}{4}\\x=\dfrac{-3\pm\sqrt[]{57}}{4}\end{matrix}\right.\)

1: \(\Leftrightarrow5x^2+4x-1-2x^2+12x-18=3x^2+5x-2-x^2-8x-16+x^2-x\)

\(\Leftrightarrow3x^2+16x-19=3x^2-4x-18\)

=>20x=1

hay x=1/20

2: \(\Leftrightarrow5x^2-20x-41=x^2-10x+25+4x^2+4x+1-\left(x^2-2x\right)+\left(x-1\right)^2\)

\(\Leftrightarrow5x^2-20x-41=4x^2-4x+26+x^2-2x+1\)

\(\Leftrightarrow-20x-41=-6x+27\)

=>-14x=68

hay x=-34/7