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VM
31 tháng 7 2019
2)
a) \(2\left|2x-3\right|=1\)
=> \(\left|2x-3\right|=1:2\)
=> \(\left|2x-3\right|=\frac{1}{2}\)
=> \(\left[{}\begin{matrix}2x-3=\frac{1}{2}\\2x-3=-\frac{1}{2}\end{matrix}\right.\) => \(\left[{}\begin{matrix}2x=\frac{1}{2}+3=\frac{7}{2}\\2x=\left(-\frac{1}{2}\right)+3=\frac{5}{2}\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=\frac{7}{2}:2\\x=\frac{5}{2}:2\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\frac{7}{4}\\x=\frac{5}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{7}{4};\frac{5}{4}\right\}.\)
b) \(7,5-3\left|5-2x\right|=-4,5\)
=> \(4,5\left|5x-2\right|=-4,5\)
=> \(\left|5x-2\right|=\left(-4,5\right):4,5\)
=> \(\left|5x-2\right|=-1\)
Ta luôn có: \(\left|x\right|>0\forall x\)
=> \(\left|5x-2\right|>-1\)
=> \(\left|5x-2\right|\ne-1\)
Vậy không tồn tại giá trị nào của \(x\) thỏa mãn yêu cầu đề bài.
c) \(\left|3x-4\right|+\left|3y+5\right|=0\)
Ta có: \(\left|3x-4\right|>\) hoặc \(=0\forall x\)
\(\left|3y+5\right|>\) hoặc \(=0\forall y.\)
=> \(\left|3x-4\right|+\left|3y+5\right|=0\)
=> \(\left[{}\begin{matrix}3x-4=0\\3y+5=0\end{matrix}\right.\) => \(\left[{}\begin{matrix}3x=0+4=4\\3y=0-5=-5\end{matrix}\right.\) => \(\left[{}\begin{matrix}x=4:3\\y=\left(-5\right):3\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\frac{4}{3}\\y=-\frac{5}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{4}{3}\right\};y\in\left\{-\frac{5}{3}\right\}.\)
Chúc bạn học tốt!
31 tháng 7 2019
Bài 1:
a) \(-15,5.20,8+3,5.9,2-15,5.9,2+3,5.20,8\)
\(=20,8.\left(-15,5+3,5\right)+9,2.\left(-15,5+3,5\right)\)
\(=\left(-15,5+3,5\right).\left(20,8+9,2\right)\)
\(=\left(-12\right).30=-360\)
b) \(\left[\left(-19,95\right)+\left(-45,75\right)\right]+\left[4,95+5,75\right]\)
\(=\left[\left(-19,95\right)+4,95\right]+\left[\left(-45,75\right)+5,75\right]\)
\(=-15+\left(-40\right)=-55\)
Bài 2 :
\(a,2.\left|2x-3\right|=1\)
\(\Leftrightarrow\left|2x-3\right|=\frac{1}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=\frac{1}{2}\\2x-3=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\frac{1}{2}+3\\2x=-\frac{1}{2}+3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\frac{7}{2}\\2x=\frac{5}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{7}{4}\\x=\frac{5}{4}\end{matrix}\right.\)
Vậy : \(x\in\left\{\frac{7}{4},\frac{5}{4}\right\}\)
\(b,7.5-3\left|5-2x\right|=-4.5\)
\(\Leftrightarrow3.\left|5-2x\right|=7.5-\left(-4.5\right)=12\)
\(\Leftrightarrow\left|5-2x\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}5-2x=4\\5-2x=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=1\\2x=9\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=\frac{9}{2}\end{matrix}\right.\)
Vậy : \(x\in\left\{\frac{1}{2},\frac{9}{2}\right\}\)
\(c,\left|3x-4\right|+\left|3y+5\right|=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-4=0\\3y+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=4\\3y=-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{4}{3}\\y=-\frac{5}{3}\end{matrix}\right.\)
Vậy : \(\left(x,y\right)=\left(\frac{4}{3},-\frac{5}{3}\right)\)
Bài 3 :
a) \(2^{300}\) và \(3^{200}\)
Ta có : \(2^{300}=\left(2^3\right)^{100}=8^{100}\)
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
mà : \(9^{100}>8^{100}\Rightarrow3^{200}>2^{300}\)
Vậy : \(3^{200}>2^{300}\)
b) \(2^{30}+3^{30}+4^{30}\) và \(3.2.4^{10}\)
Ta có : \(3.2.4^{10}=6.\left(2^2\right)^{10}=6.2^{20}=3.2^{21}\)
Ta thấy : \(2^{30}>3.2^{21}\Rightarrow2^{30}+3^{30}+4^{30}>3.2^{21}\)
hay : \(2^{30}+3^{30}+4^{30}>3.2.4^{10}\)
Vậy : \(2^{30}+3^{30}+4^{30}>3.2.4^{10}\)
Chúc bạn học tốt !
1 tháng 11 2019
2a) \(\frac{3^6+45^4-15^3.4^5}{27^4.25^3+45^6}\)
= \(\frac{3^6+\left(3^2.5\right)^4-\left(3.5\right)^3.\left(2^2\right)^5}{\left(3^3\right)^4.\left(5^2\right)^3+\left(3^2.5\right)^6}\)
= \(\frac{3^6+3^8.5^4-3^3.5^3.4^{10}}{3^{12}.5^6-3^{12}.5^6}=\frac{3^3.\left(3^3+3^5.5^4-5^3.4^{10}\right)}{0}\)(xem lại đề)
b) \(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{16}{3}\right)^3:\left(\frac{4}{9}\right)^3}{2^7.5^2+512}\)
= \(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{16}{3}:\frac{4}{9}\right)^3}{2^7.5^2+2^9}\)
= \(\frac{2^7+12^3}{2^7\left(5^2+2^2\right)}\)
= \(\frac{2^7+\left(2^2.3\right)^3}{2^7.29}\)
= \(\frac{2^7+2^6.3^3}{2^7.29}\)
= \(\frac{2^6\left(1+27\right)}{2^7.29}=\frac{28}{2.29}=\frac{14}{29}\)
KH
22 tháng 9 2018
* Trả lời:
\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)
\(\Leftrightarrow-3+6x-4-12x=-5x+5\)
\(\Leftrightarrow6x-12x+5x=3+4+5\)
\(\Leftrightarrow x=12\)
\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)
\(\Leftrightarrow6x-15-6+24x=-3x+7\)
\(\Leftrightarrow6x+24x+3x=15+6+7\)
\(\Leftrightarrow33x=28\)
\(\Leftrightarrow x=\dfrac{28}{33}\)
\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)
\(\Leftrightarrow1-3x-6x+12=-4x-5\)
\(\Leftrightarrow-3x-6x+4x=-1-12-5\)
\(\Leftrightarrow-5x=-18\)
\(\Leftrightarrow x=\dfrac{18}{5}\)
\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)
\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)
\(\Leftrightarrow-x-5x=-7\)
\(\Leftrightarrow-6x=-7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)
\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)
\(\Leftrightarrow-15x+3x=4\)
\(\Leftrightarrow-12x=4\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
21 tháng 7 2017
\(2x+\frac{1}{2}=\frac{-5}{3}\)
\(2x=\frac{-5}{3}-\frac{1}{2}\)
\(2x=\frac{-10}{6}-\frac{3}{6}\)
\(2x=\frac{-13}{6}\)
\(x=\frac{-13}{6}:2\)
\(x=\frac{-13}{12}\)
MS
3
16 tháng 7 2019
a) |5x - 1| - x = 2x + 3
<=> |5x - 1| = 2x + 3 + x
<=> |5x - 1| = 3x + 3
<=> 5x - 1 = 3x + 3 hoặc 5x - 1 = -(3x + 3)
5x - 1 - 3x = 3 5x - 1 + 3x = -3
2x - 1 = 3 8x - 1 = -3
2x = 3 + 1 8x = -3 + 1
2x = 4 8x = -2
x = 2 x = -2/8 = -1/4
=> x = 2 hoặc x = -1/4
16 tháng 7 2019
b) Ta có: |2x + 1| \(\ge\)0 \(\forall\)x
|x - 3| \(\ge\)0 \(\forall\)x
|2x+ 3| \(\ge\)0 \(\forall\)x
=> |2x + 1| + |x - 3| + |2x + 3| \(\ge\)0 \(\forall\)x
=> x - 5 \(\ge\)0 \(\forall\)x => x \(\ge\)5 \(\forall\)x
Với x \(\ge\)5
=> 2x + 1 + x - 3 + 2x + 3 = x - 5
=> 4x + 1 = x - 5
=> 4x - x = -5 - 1
=> 3x = -6
=> x = -2 (ktm)
Vậy ko có giá trị thõa mãn