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Bài 1:
a, \(\left(x-2\right)^2=9\)
\(\Rightarrow x-2\in\left\{-3;3\right\}\Rightarrow x\in\left\{-1;5\right\}\)
b, \(\left(3x-1\right)^3=-8\)
\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)
\(\Rightarrow x=-\dfrac{1}{3}\)
c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow x+\dfrac{1}{2}\in\left\{-\dfrac{1}{4};\dfrac{1}{4}\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{3}{4};-\dfrac{1}{4}\right\}\)
d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)
Vì \(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)
e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)
Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)
f, \(\left(\dfrac{1}{2}\right)^{2x-1}=8\) \(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^{-3}\) Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(2x-1=-3\) \(\Rightarrow2x=-2\Rightarrow x=-1\) Chúc bạn học tốt!!!
\(x+8-(x+22)=x+8-x-22=8-22=-14\)
\(-(x+5)+(x+10)-5=-x-5+x+10-5=0\)
1*5* \(⋮\)2;3;5;6;9
Vì 1*5* chia hết cho 2 và 5 nên dấu sao cuối cùng=0
Ta có: 1*5* chia hết cho 6=> chia hết cho 3 và 2
1*5* chia hết cho 9
1*50 chia hết cho 9
1+*+5+0 chia hết cho 9
6+* chia hết cho 9=> *=3
vậy số cần tìm là 1350
\(\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{5.7}+.....+\dfrac{5}{99.101}\)
\(=\dfrac{5}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+.....+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=\dfrac{5}{2}.\left(1-\dfrac{1}{101}\right)=\dfrac{5}{2}.\dfrac{100}{101}=\dfrac{250}{101}\)
Để \(A\in Z\)thì
\(n+2⋮n-5\)
\(n-5+7⋮n-5\)
\(\Leftrightarrow7⋮n-5\)
\(\Leftrightarrow n-5\inƯ\left(7\right)\)
\(Ư\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(n\in\left\{6;4;12;-2\right\}\)
1 bỏ dấu ngoặc rồi tính :
a) x+ 8 - ( x + 22)
= x + 8 - x - 22
= -14
b) -(x+5) + (x + 10 ) - 5
= -x - 5 + x + 10 -5
= 0
a: \(\Leftrightarrow-\dfrac{5}{4}x+\dfrac{3}{7}=\dfrac{6}{5}x-\dfrac{1}{2}\)
=>-49/20x=-13/14
hay x=130/343
c: \(\left|y+\dfrac{9}{25}\right|+\left|x-y\right|=0\)
=>x-y=0 và y+9/25=0
=>x=y=-9/25
d: ||x+5|-4|=3
=>|x+5|-4=-3 hoặc |x+5|-4=3
=>|x+5|=1 hoặc |x+5|=7
\(\Leftrightarrow x+5\in\left\{1;-1;7;-7\right\}\)
hay \(x\in\left\{-4;-6;2;-12\right\}\)
\(\dfrac{1}{2}.2^n+4.2^n=9.5^n\)
\(2^{n-1}+2^{n+2}=9.5^n\)
ặc xem kĩ lại đề xem nhé
a) \(-\dfrac{2}{3}\left(x-\dfrac{1}{4}\right)=\dfrac{1}{3}\left(2x-1\right)\)
\(\Rightarrow-\dfrac{2}{3}x+\dfrac{1}{6}=\dfrac{2}{3}x-\dfrac{1}{3}\)
\(\Rightarrow\dfrac{1}{6}+\dfrac{1}{3}=\dfrac{2}{3}x+\dfrac{2}{3}x\)
\(\Rightarrow\dfrac{1}{2}=\dfrac{4}{3}x\)
\(\Rightarrow x=\dfrac{1}{2}:\dfrac{4}{3}=\dfrac{3}{8}\)
Vậy \(x=\dfrac{3}{8}\).
1. \(\dfrac{16.17-5}{16.16-1}:\left(x-\dfrac{2}{3}\right)=\dfrac{1}{3}\)
<=> \(\dfrac{272-5}{256-1}:\left(x-\dfrac{2}{3}\right)=\dfrac{1}{3}\)
<=> \(\dfrac{267}{255}:\left(x-\dfrac{2}{3}\right)=\dfrac{1}{3}\)
<=> x - \(\dfrac{2}{3}=\dfrac{267}{85}\)
<=> x = \(\dfrac{971}{255}\)
@Triều Nguyễn Quốc
2. a, 8\(\dfrac{1}{5}\left(11\dfrac{94}{1591}-6\dfrac{38}{1517}\right):8\dfrac{11}{13}\)
= \(\dfrac{41}{5}\left(5\dfrac{60}{1763}\right):\dfrac{355}{43}\)
= \(\dfrac{41}{5}.\dfrac{8875}{1763}:\dfrac{355}{43}\)
= \(\dfrac{1775}{43}:\dfrac{355}{43}\)
= 5
@Triều Nguyễn Quốc
\(\Leftrightarrow2^{x+1}.3^y=4^x.3^x\)
\(\Leftrightarrow2^{x+1}.3^y=2^{2x}.3^x\)
\(\Leftrightarrow\frac{3^y}{3^x}=\frac{2^{2x}}{2^{x+1}}\)
\(\Leftrightarrow3^{y-x}=2^{x-1}\)
Nếu \(x>1\Rightarrow\) vế trái lẻ, vế phải chẵn pt vô nghiệm
\(\Rightarrow x=1\Rightarrow3^{y-1}=1\Rightarrow y=1\)
like nha bằng 4 nhé