c/ [ 3 - x]10x : [3 - x]20=1
d/ [ x - 6 ]3 = [x - 6]2
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12 tháng 8 2021
\(a,\dfrac{5}{-x^2+5x-6}+\dfrac{x+3}{2-x}=0\left(x\ne2;x\ne3\right)\\ \Leftrightarrow\dfrac{5}{\left(x-3\right)\left(x-2\right)}-\dfrac{x+3}{x-2}=0\\\Leftrightarrow\dfrac{5-\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x-2\right)}=0 \\ \Leftrightarrow5-x^2+9=0\\ \Leftrightarrow14-x^2=0\\ \Leftrightarrow x^2=14\\ \Leftrightarrow\left[{}\begin{matrix}x=\sqrt{14}\\x=-\sqrt{14}\end{matrix}\right.\)
\(b,\dfrac{x}{2x+2}-\dfrac{2x}{x^2-2x-3}=\dfrac{x}{6-2x}\left(x\ne-1;x\ne3\right)\\ \Leftrightarrow\dfrac{x}{2\left(x+1\right)}-\dfrac{2x}{\left(x-3\right)\left(x+1\right)}=\dfrac{x}{2\left(3-x\right)}\\ \Leftrightarrow\dfrac{x\left(x-3\right)-2x\cdot2}{2\left(x-3\right)\left(x+1\right)}=\dfrac{-x\left(x+1\right)}{2\left(x-3\right)\left(x+1\right)}\\ \Leftrightarrow x^2-3x-4x=-x^2-x\\ \Leftrightarrow2x^2-6x=0\\ \Leftrightarrow2x\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
\(c,\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\left(x\ne1\right)\\ \Leftrightarrow\dfrac{x^2+x+1-3x^2}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\\ \Leftrightarrow-2x^2+x+1=2x^2-2x\\ \Leftrightarrow4x^2-3x-1=0\\ \Leftrightarrow\left(x-1\right)\left(4x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{4}\end{matrix}\right.\)
\(d,\dfrac{x+25}{2x^2-50}-\dfrac{x+5}{x^2-5x}=\dfrac{5-x}{2x^2+10x}\left(x\ne5;x\ne-5\right)\\ \Leftrightarrow\dfrac{x+25}{2\left(x-5\right)\left(x+5\right)}-\dfrac{x+5}{x\left(x-5\right)}=\dfrac{5-x}{2x\left(x+5\right)}\\ \Leftrightarrow\dfrac{x^2+25x-2\left(x+5\right)^2}{2x\left(x-5\right)\left(x+5\right)}=\dfrac{\left(5-x\right)\left(x-5\right)}{2x\left(x+5\right)\left(x-5\right)}\\ \Leftrightarrow x^2+25x-2\left(x^2+10x+25\right)=-\left(x^2-10x+25\right)\\ \Leftrightarrow x^2+25x-2x^2-20x-50=-x^2+10x-25\\ \Leftrightarrow-5x=25\\ \Leftrightarrow x=-5\)
Tick nha
6 tháng 8 2023
a: A=(-x)^3+3*(-x)^2*2+3*(-x)*2^2+2^3=(-x+2)^3
=(28+2)^3=30^3=27000
b: \(C=\left(x+2y-2\right)^3=\left(20+2\cdot9-2\right)^3\)
=36^3
c: 11^3-1
=(11-1)(11^2+11+1)
=10*(121+12)
=1330
d: x^3-y^3=(x-y)^3+3xy(x-y)
=6^3+3*6*9
=216+162
=378
BT
14 tháng 10 2023
a) (3x-15)7 = 0
3x-15 = 0
3x = 0+15
3x = 15
x = 15:3
x = 5
b) 42x-6 = 1
2x-6 = 0
2x = 0+6
2x = 6
x = 6:2
x = 3
c) Tớ ko bít
d) (x - 6)3 = (x - 6)2
Th1:
x - 6 = 1
x = 1 + 6
x = 7
Th2:
x - 6 = 0
x = 6
Vậy x = 7
x = 6
--thodagbun--
BN
14 tháng 10 2023
a, (3x-15)^7=0 <=> 3x-15=0 <=> x=5
b, 42x+6=1 <=> 16x=-5 <=>x=-5/16
c, \(\dfrac{\left(3-x\right)^{10x}}{\left(3-x\right)^{20}}=1\Leftrightarrow\left(3-x\right)^{10x-20}=1\)
TH1: 10x-20 = 0 <=> x=2
TH2: 3-x=1 <=> x=2
Vậy x=2
d, (x-6)^3 = (x-6)^2
<=> (x-6)^2.[(x-6)-1]=0
<=> (x-6)^2=0 hoặc (x-6)-1=0
<=> x=6 hoặc x=7
TN
21 tháng 7 2017
b ) -2(3x+2)-3 =28
-6x-4-3=28
-6x = 28 +4+3
-6x = 35
x =\(\dfrac{35}{-6}\)= \(\dfrac{-35}{6}\)= -5,8
vậy x= -5,8
c ) -(x+3)-5(x-7)=10x-20
-(x+3)-5x+35=10x-20
-x+3-5x+35=10x-20
-x-5x-10x=-20-3-35
-16x=-58
x=\(\dfrac{-58}{-16}\)=\(\dfrac{58}{16}\)=3,625
vậy x =3,625
d)2x+37=-6(3x-8)
2x+37=-18x+48
2x+18x=48-37
20x=11
x=\(\dfrac{11}{20}\)=0,55
vậy x=0,55
11 tháng 1 2023
a: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x+1+1}{x+1}+\dfrac{2}{y-2}=6\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+1}+\dfrac{2}{y-2}=5\\\dfrac{5}{x+1}-\dfrac{1}{y-2}=3\end{matrix}\right.\)
=>x+1=1 và y-2=1/2
=>x=0 và y=5/2
b: \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x-2y}=\dfrac{1}{2}-\dfrac{1}{18}=\dfrac{9}{18}-\dfrac{1}{18}=\dfrac{8}{18}=\dfrac{4}{9}\\\dfrac{2}{2x-y}=\dfrac{1}{18}+\dfrac{1}{x-2y}\end{matrix}\right.\)
=>x-2y=9 và 2/2x-y=1/18+1/9=1/18+2/18=3/18=1/6
=>x-2y=9 và 2x-y=12
=>x=5; y=-2
c: \(\Leftrightarrow\left\{{}\begin{matrix}10\left|x-6\right|+15\left|y+1\right|=25\\10\left|x-6\right|-8\left|y+1\right|=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23\left|y+1\right|=23\\\left|x-6\right|=1\end{matrix}\right.\)
=>|x-6|=1 và |y+1|=1
=>\(\left\{{}\begin{matrix}x\in\left\{7;5\right\}\\y\in\left\{0;-2\right\}\end{matrix}\right.\)
c) [3 - x]^10x : [3 - x]^20 = 1
Ta thấy [3 - x]^10x : [3 - x]^20 = 1 => [3 - x]^10x = [3 - x]^20 vì a : a = 1
[3 - x](1) = [3 - x](2) nên ta không xét, vậy ta chỉ xét hai số mũ 10x và 20
10x = 20 => x = 20 : 10 => x = 2
Vậy x = 2
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