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\(15-\left\{2.\left[\left(2x-4\right).5\right].3.\left(x+1\right)\right\}=12-x\)
\(15-\left\{\left[10x-20\right].6.\left(x+1\right)\right\}=12-x\)
\(15-\left\{10x-20.6x+1\right\}=12-x\)
\(15-\left\{10x-120x+1\right\}=12-x\)
\(15-\left(-110x\right)-1=12-x\)
\(15+110x-1=12-x\)
\(110x+x=12-15+1\)
\(111x=-2\)
\(x=\dfrac{-2}{111}\)
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1: \(\Leftrightarrow x^2-4x+4-2\left(x^2+2x+1\right)=\left(2x+1\right)\left(1-3x\right)+2x\left(x-1\right)\)
\(\Leftrightarrow x^2-4x+4-2x^2-4x-2=\left(2x-6x^2+1-3x\right)+2x^2-2x\)
\(\Leftrightarrow-x^2-8x+2=-6x^2-x+1+2x^2-2x\)
\(\Leftrightarrow-x^2-8x+2=-4x^2-3x+1\)
\(\Leftrightarrow3x^2-5x+1=0\)
\(\Delta=\left(-5\right)^2-4\cdot3\cdot1=25-12=13>0\)
Do đó: Phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{5-\sqrt{13}}{6}\\x_2=\dfrac{5+\sqrt{13}}{6}\end{matrix}\right.\)
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1. a, 3x + |x - 2| = 8
<=> |x - 2| = 8 - 3x
Xét 2 TH :
TH1: x - 2 = 8 - 3x
<=> x + 3x = 8 + 2
<=> 4x = 10
<=> x = \(\dfrac{5}{2}\) (thỏa mãn)
TH2: x - 2 = -(8 - 3x)
<=> x - 2 = -8 + 3x
<=> -2 + 8 = 3x - x
<=> 6 = 2x
<=> x = 3 (thỏa mãn)
b, 5 - |x - 1| = 4
<=> |x - 1| = 1
<=> \(\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\) (thỏa mãn)
@Nguyễn Hoàng Vũ
2. 5.(x - 2) - 4.(1 - 3x) = |3 - 7| + 2.(1 + 2x)
<=> 5x - 10 - 4 + 12x = 4 + 2 + 4x
<=> 17x - 14 = 6 + 4x
<=> 17x - 4x = 6 + 14
<=> 13x = 20
<=> x = \(\dfrac{20}{13}\) (thỏa mãn)
@Nguyễn Hoàng Vũ
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\(\Leftrightarrow\dfrac{2}{3}x+\dfrac{4}{3}-\dfrac{5}{4}x+\dfrac{5}{4}=\dfrac{15}{2}-\dfrac{3}{2}x-\dfrac{3}{2}\left(2x+3\right)\)
\(\Leftrightarrow x\cdot\dfrac{-7}{12}+\dfrac{31}{12}=\dfrac{-15}{2}x+3\)
=>83/12x=5/12
hay x=5/83
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Bài 1:
\(\left(-\dfrac{72}{40}-\dfrac{144}{60}-2\dfrac{1}{3}\right):\left(\dfrac{45}{100}-\dfrac{25}{60}+-\dfrac{75}{25}\right)\)
\(=\left(-\dfrac{9}{5}-\dfrac{12}{5}-\dfrac{7}{3}\right):\left(\dfrac{9}{20}-\dfrac{5}{12}+-3\right)\)
\(=\left(-\dfrac{27}{15}-\dfrac{36}{15}-\dfrac{21}{15}\right):\left(\dfrac{27}{60}-\dfrac{25}{60}+-3\right)\)
\(=\left(-\dfrac{28}{5}\right):\left(-\dfrac{89}{30}\right)\)
\(=\left(-\dfrac{28}{5}\right).\left(-\dfrac{30}{89}\right)\)
\(=\dfrac{168}{89}\)
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a ) ( x + 1 ) x ( x2 - 4 ) = 0
vậy chắc chắn 1 biểu thức phải bằng 0 để có kết quả đúng . vậy chỉ có thể là x2 - 4 = 0
vì phép còn lại là x + 1 = số nguyên dương
x2 - 4 = 0
x = 2
b ) x15 = x
vậy quá rõ x = 1 , 0
vì chỉ có 2 số này nhân bao nhiêu lần chính nó cũng bằng nó
c ) ( x - 5 ) 4 = ( x - 5 )6
4 x - 625 = 6 x - 15625
4 x + 15625 - 625 = 6 x
4 x + 15000 = 6 x
15000 = 2 x
x = 7500
d ) làm sau
a. \(\left(x+1\right)\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
TH1: \(x+1=0\Rightarrow x=-1\)
TH2: \(x-2=0\Rightarrow x=2\)
TH3: \(x+2=0\Rightarrow x=-2\)
Vậy:...
b) \(x^{15}=x\)
\(\Rightarrow x\in\left\{0;1;-1\right\}\)
c) \(\left(x-5\right)^4=\left(x-5\right)^6\)
TH1:\(x-5=1\Rightarrow x=6\)
TH2: \(x-5=-1\Rightarrow x=4\)
TH3: \(x-5=0\Rightarrow x=5\)
d) \(\left(2x+1\right)^3=125\)
\(\Leftrightarrow2x+1=\sqrt[3]{125}=5\)
\(\Leftrightarrow x=2\)
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\(\dfrac{11.3^{22}.3^7-9^{15}}{\left(2.3^{14}\right)^2}\)
\(=\dfrac{11.3^{29}-\left(3^2\right)^{15}}{2^2.3^{28}}\)
\(=\dfrac{11.3^{29}-3^{30}}{2^2.3^{28}}\)
\(=\dfrac{3^{29}\left(11-3\right)}{2^2.3^{28}}\)
\(=\dfrac{3^{29}.2^3}{2^2.3^{28}}\)
\(=\dfrac{3.2}{1.1}=6\)
`( 2x - 1 ) . ( 15 - x ) = 0`
`@TH1: 2x - 1 = 0`
`=> 2x = 1`
`=> x = 1 / 2`
`@TH2: 15 - x = 0`
`=> x = 15`
Vậy `x = 1 / 2` hoặc `x = 15`
\(\left(2x-1\right)\cdot\left(15-x\right)=0\)
\(TH1:2x-1=0\)
\(2x=0+1\)
\(2x=1\)
\(x=1:2\)
\(x=\dfrac{1}{2}\)
\(TH2:15-x=0\)
\(x=15-0\)
\(x=15\)
Vậy \(x=\left[{}\begin{matrix}\dfrac{1}{2}\\15\end{matrix}\right.\)