2*3x+1 - 3x =135
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\(\left(3x-5y\right)^2+\left(xy-135\right)^2=0\)
Vì \(\left\{{}\begin{matrix}\left(3x-5y\right)^2\ge0\forall x,y\\\left(xy-135\right)^2\ge0\forall x,y\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}3x-5y=0\\xy-135=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}y\\xy=135\end{matrix}\right.\)
\(\Rightarrow\dfrac{5}{3}y.y=135\)\(\Rightarrow y^2=81\)
\(\Leftrightarrow\left[{}\begin{matrix}y=9\Rightarrow x=15\\y=-9\Rightarrow x=-15\end{matrix}\right.\)
Ta có: \(\left(3x-5y\right)^2\ge0\forall x;y\)
\(\left(xy-135\right)^2\ge0\forall x;y\)
\(\Rightarrow\left(3x-5y\right)^2+\left(xy-135\right)^2\ge0\forall x\)
Mặt khác: \(\left(3x-5y\right)^2+\left(xy-135\right) ^2=0\)
nên: \(\left\{{}\begin{matrix}\left(3x-5y\right)^2=0\\\left(xy-135\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-5y=0\\xy-135=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=5y\\xy=135\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}y\\\dfrac{5}{3}y^2=135\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}y\\y^2=81\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}y\\\left[{}\begin{matrix}y=9\\y=-9\end{matrix}\right.\end{matrix}\right.\)
\(+,TH1:y=9\Leftrightarrow x=\dfrac{5}{3}\cdot9=15\left(tm\right)\)
\(+,TH2:y=-9\Leftrightarrow x=\dfrac{5}{3}\cdot\left(-9\right)=-15\left(tm\right)\)
Vậy ...
#\(Toru\)
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+) \(24+\left(x-6\right)=135\)
\(\Rightarrow x-6=135-24=111\)
\(\Rightarrow x=111+6=117\)
+) \(2019-2\cdot\left(3x-2\right)=19\)
\(\Rightarrow2\cdot\left(3x-2\right)=2019-19=2000\)
\(\Rightarrow3x-2=2000:2=1000\)
\(\Rightarrow3x=1000+2=1002\)
\(\Rightarrow x=1002:3\)
\(\Rightarrow x=334\)
+) \(3^x+3^{x+1}=324\)
\(\Rightarrow3^x+3^x\cdot3=324\)
\(\Rightarrow3^x\cdot\left(1+3\right)=324\)
\(\Rightarrow3^x\cdot4=324\) \(\Rightarrow3^x=324:4=81\)
\(\Rightarrow3^x=3^4\) \(\Rightarrow x=4\)
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a) \(\left(2x+7\right)+135=0\)
\(2x+7=0-135\)
\(2x+7=-135\)
\(2x=-135-7\)
\(2x=-142\)
\(x=-142:2\)
\(x=-71\left(tm\right)\)
Vậy \(x=-71\)
a) (2x+7) + 135 = 0
2x+7= -135
2x= -135-7
2x=-142
x= -142 : 2=-71
b) (162 +3x) +(x-2)=0
162+ 3x + x-2=0
162+ x(3+1)-2=0
x.4= 0-162 +2
x.4= -160
x= -160: 4= -40
Chúc bạn học tốt
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Ta có 3x+45=150%x+135
3x+45=1,5x+135
3x-1,5x=135-45
1,5x=90
x=90:1,5
x=60
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Lời giải:
1. $(x+2)-2=0$
$x+2=2$
$x=0$
2.
$(x+3)+1=7$
$x+3=7-1=6$
$x=6-3=3$
3.
$(3x-4)+4=12$
$3x-4+4=12$
$3x=12$
$x=12:3=4$
4.
$(5x+4)-1=13$
$5x+4=13+1=14$
$5x=14-4=10$
$x=10:5=2$
5.
$(4x-8)-3=5$
$4x-8=5+3=8$
$4x=8+8=16$
$x=16:4=4$
6.
$3+(x-5)=7$
$x-5=7-3=4$
$x=4+5=9$
7.
$8-(2x-4)=2$
$2x-4=8-2=6$
$2x=6+4=10$
$x=10:2=5$
8.
$7+(5x+2)=14$
$5x+2=14-7=7$
$5x=7-2=5$
$x=5:5=1$
9.
$5-(3x-11)=1$
$3x-11=5-1=4$
$3x=11+4=15$
$x=15:3=5$
10.
$16-(8x+2)=6$
$8x+2=16-6=10$
$8x=10-2=8$
$x=8:8=1$
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\(3x=5y\Rightarrow\frac{x}{5}=\frac{y}{3}\)
ÁP DỤNG DÃY TỈ SỐ BẰNG NHAU TA CÓ
\(\frac{x}{5}=\frac{y}{3}=\frac{xy}{15}=\frac{135}{15}=9\)
\(\Rightarrow\hept{\begin{cases}x=45\\y=27\end{cases}}\)
\(2.3^{x+1}-3^x=135\)
\(3^x\left(2.3-1\right)=135\)
\(3^x=27\)
\(x=3\)
2.3ˣ⁺¹ - 3ˣ = 135
3ˣ.(2.3 - 1) = 135
3ˣ.5 = 135
3ˣ = 135 : 5
3ˣ = 27
3ˣ = 3³
x = 3