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a) ( x - 3 )2 - 4 = 0
<=> ( x - 3 )2 = 4
<=> \(\orbr{\begin{cases}\left(x-3\right)^2=2^2\\\left(x-3\right)^2=\left(-2\right)\end{cases}}\)
<=> \(\orbr{\begin{cases}x-3=2\\x-3=-2\end{cases}}\)
<=> \(\orbr{\begin{cases}x=5\\x=1\end{cases}}\)
Vậy S = { 5 ; 1 }
b) x2 - 9 = 0
<=> x2 = 9
<=> \(\orbr{\begin{cases}x^2=3^2\\x^2=\left(-3\right)^2\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-3\end{cases}}\)
Vậy S = { 3 ; -3 }
c) x( x - 2x ) - x2 - 8 = 0
<=> x2 - 2x2 - x2 - 8 = 0
<=> -2x2 - 8 = 0
<=> -2x2 = 8
<=> x2 = -4 ( vô lí )
<=> x = \(\varnothing\)
Vậy S = { \(\varnothing\)}
d) 2x( x - 1 ) - 2x2 + x - 5 = 0
<=> 2x2 - 2x - 2x2 + x - 5 = 0
<=> -x - 5 = 0
<=> -x = 5
<=> x = -5
Vậy S = { -5 }
e) x( x - 3 ) - ( x + 1 )( x - 2 ) = 0
<=> x2 - 3x - ( x2 - x - 2 ) = 0
<=> x2 - 3x - x2 + x + 2 = 0
<=> - 2x + 2 = 0
<=> -2x = -2
<=> x = 1
Vậy S = { 1 }
f) x( 3x - 1 ) - 3x2 - 7x = 0
<=> 3x2 - x - 3x2 - 7x = 0
<=> -8x = 0
<=> x = 0
Vậy S = { 0 }
a) x(x-1) - (x+1)(x+2) = 0
x\(^2\)- x -x\(^{^2}\)-2x +x+2=0
-2x+2=0
-2x=0+2
-2x=2
x=-1
Vậy x bằng -1
Bài 1.
a: \(x\in\left\{0;25\right\}\)
c: \(x\in\left\{0;5\right\}\)
\(a,\Leftrightarrow2x^2+10x-2x^2=12\Leftrightarrow x=\dfrac{12}{10}=\dfrac{6}{5}\\ b,\Leftrightarrow\left(5-2x-4\right)\left(5-2x+4\right)=0\\ \Leftrightarrow\left(1-2x\right)\left(9-2x\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{9}{2}\end{matrix}\right.\\ c,\Leftrightarrow3x^2-3x^2+6x=36\Leftrightarrow x=6\\ d,\Leftrightarrow2\left(x+5\right)-x\left(x+5\right)=0\\ \Leftrightarrow\left(2-x\right)\left(x+5\right)=0\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\\ e,\Leftrightarrow4x^2-4x+1-4x^2+196=0\\ \Leftrightarrow-4x=-197\Leftrightarrow x=\dfrac{197}{4}\)
\(f,\Leftrightarrow x^2+8x+16-x^2+1=16\Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\\ g,Sửa:\left(3x+1\right)^2-\left(x+1\right)^2=0\\ \Leftrightarrow\left(3x+1-x-1\right)\left(3x+1+x+1\right)=0\\ \Leftrightarrow2x\left(4x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\\ h,\Leftrightarrow x^2+8x-x-8=0\\ \Leftrightarrow\left(x+8\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-8\end{matrix}\right.\\ i,\Leftrightarrow2x^2-13x+15=0\\ \Leftrightarrow2x^2+2x-15x-15=0\\ \Leftrightarrow\left(x+1\right)\left(2x-15\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{15}{2}\end{matrix}\right.\)
\(a,\left(2x+1\right)\left(x^2+2\right)=0\)
\(\left[{}\begin{matrix}2x=-1\\x^2=-2\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=-\frac{1}{2}\\x=\pm\sqrt{2}\end{matrix}\right.\)
\(b,\left(x^2+x+1\right)\left(6-2x\right)=0\)
\(6-2x=0\Leftrightarrow2x=6\Leftrightarrow x=3\)
\(c,\left(x-5\right)\left(3-2x\right)\left(3x+4\right)=0\)
\(\left[{}\begin{matrix}x-5=0\\3-2x=0\\3x+4=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=5\\2x=3\\3x=-4\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=5\\x=\frac{3}{2}\\x=-\frac{4}{3}\end{matrix}\right.\)
\(d,\left(x^2+4\right)\left(7x-3\right)=0\)
\(\left[{}\begin{matrix}x^2+4=0\\7x-3=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x^2=-4\\7x=3\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=\pm2\left(voli\right)\\x=\frac{3}{7}\end{matrix}\right.\)
\(e,\left(8x-4\right)=\left(x^2+x+2\right)\)
\(8x-4=x^2+x+2\)
\(8x-4-x^2-x-2=0\)
\(7x-6-x^2=0\)
\(\left(x-6\right)\left(x-1\right)=0\)
\(\left[{}\begin{matrix}x-6=0\\x-1=0\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=6\\x=1\end{matrix}\right.\)
\(f,\left(2x-1\right)\left(3x+2\right)\left(5-x\right)\)
đề thiếu hay là rút gọn vậy bn
`a,4x-10=0 `
`<=> 4x=10`
`<=>x=10/4`
`<=>x=5/2`
`b, 7-3x=9-x `
`<=>-3x+x=9-7`
`<=>-2x=2`
`<=>x=-1`
`c, 2x-(3-5x) = 4(x+3)`
`<=>2x-3+5x=4x+12`
`<=>2x+5x-4x=12+3`
`<=>3x=15`
`<=>x=5`
`d, 5-(6-x)=4(3-2x) `
`<=>5-6+x=12-8x`
`<=>x+8x=12-5+6`
`<=>9x=13`
`<=>x=13/9`
`e, 4(x+3)=-7x+17 `
`<=>4x+12=-7x+17`
`<=>4x+7x=17-12`
`<=>11x=5`
`<=>x=5/11`
`f, 5(x-3) - 4=2(x-1)+7`
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`g, 5(x-3)-4=2(x-1)+7 `
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`h,4(3x-2)-3(x-4)=7x+20`
`<=>12x-8-3x+12=7x+20`
`<=>12x-3x-7x=20+8+12`
`<=>2x=40`
`<=>x=20`
1.a) \(\Leftrightarrow\) 3x+10-2x =0
\(\Leftrightarrow\text{ 3x-2x=-10}\)
\(\Leftrightarrow x=-10\)
b) coi lại có thiếu ngoặc ko nhé
cứ nhân vào dấu ngoặc rồi làm như thường
a. (x-4)\(^2\)=x+1
⇔ x\(^2\) - 8x + 16 -x - 1 =0
⇔ x\(^2\) - 9x + 15 = 0
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{9+\sqrt{21}}{2}\\x=\frac{9-\sqrt{21}}{2}\end{matrix}\right.\)
b. 5.(x+3)+2x.(3+x)=0
⇔ (5+ 2x ) ( x + 3 ) =0
\(\Leftrightarrow\left[{}\begin{matrix}5+2x=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{-5}{2}\\x=-3\end{matrix}\right.\)
c. (x-4)\(^2\)-36=0
⇔ ( x - 4 - 6 ) ( x - 4 + 6 ) = 0
⇔ ( x - 10 ) ( x + 2 ) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x-10=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)
d. (7x-4)\(^2\)-(2x+1)\(^2\)=0
⇔ ( 7x - 4 - 2x - 1 ) ( 7x - 4 + 2x + 1 ) = 0
⇔ ( 5x - 5 ) ( 9x - 3 ) = 0
\(\Leftrightarrow\left[{}\begin{matrix}5x-5=0\\9x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{1}{3}\end{matrix}\right.\)
a. (x-4)22=x+1
⇔ x22 - 8x + 16 -x - 1 =0
⇔ x22 - 9x + 15 = 0
⇔⎡⎣x=9+√212x=9−√212⇔[x=9+212x=9−212
b. 5.(x+3)+2x.(3+x)=0
⇔ (5+ 2x ) ( x + 3 ) =0
⇔[5+2x=0x+3=0⇔[x=−52x=−3⇔[5+2x=0x+3=0⇔[x=−52x=−3
c. (x-4)22-36=0
⇔ ( x - 4 - 6 ) ( x - 4 + 6 ) = 0
⇔ ( x - 10 ) ( x + 2 ) = 0
⇔[x−10=0x+2=0⇔[x=10x=−2⇔[x−10=0x+2=0⇔[x=10x=−2
d. (7x-4)22-(2x+1)22=0
⇔ ( 7x - 4 - 2x - 1 ) ( 7x - 4 + 2x + 1 ) = 0
⇔ ( 5x - 5 ) ( 9x - 3 ) = 0
⇔[5x−5=09x−3=0⇔[x=1x=13