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câu hỏi hay......nhưng tui xin nhường cho các bn khác
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THANKS
\(x\cdot\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x-1=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
\(\left(x+1\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x-2=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)
\(x\cdot\left(x-2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x=0\\x-2=0\\x-3=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=0\\x=2\\x=3\end{cases}}\)
Phần cuối thay dấu ngoặc nhọn bằng dấu ngoặc vuông nha .
\(6\cdot x-5=613\)
\(6\cdot x=613+5\)
\(6\cdot x=618\)
\(x=618\div6\)
\(x=103\)
Vậy \(x=103\)
\(12\cdot x+3\cdot x=30\)
\(x\cdot\left(12+3\right)=30\)
\(x\cdot15=30\)
\(x=30\div15\)
\(x=2\)
Vậy \(x=2\)
\(125-25\cdot\left(x-1\right)=100\)
\(25\cdot\left(x-1\right)=125-100\)
\(25\cdot\left(x-1\right)=25\)
\(x-1=25\div25\)
\(x-1=1\)
\(x=1+1\)
\(x=2\)
Vậy \(x=2\)
\(\left(x-2\right)\cdot\left(x-14\right)=0\)
\(\Rightarrow\) \(x-2=0\) hoặc \(x-14=0\)
TH1: \(x-2=0\) TH2: \(x-14=0\)
\(x=0+2\) \(x=0+14\)
\(x=2\) \(x=14\)
Vậy \(x=2\) hoặc \(x=14\)
\(128-3\cdot\left(x+4\right)=23\)
\(3\cdot\left(x+4\right)=128-23\)
\(3\cdot\left(x+4\right)=105\)
\(x+4=105\div3\)
\(x+4=35\)
\(x=35-4\)
\(x=31\)
Vậy \(x=31\)
12.x+3.x=30
x.(12+3)=30
x.15=30
x =30:15
x =2
125-25.(x-1)=100
25.(x-1)=125-100
25.(x-1)=25
x-1=25:25
x-1=1
x =1+1
x=2
(x-2).(x-14)=0
x=14
128-3.(x+4)=23
3.(x+4)=128-23
3.(x+4)=105
x+4=105:3
x+4=35
x = 35+4
x =39
Bài 1 :
\(A=3^0+3^1+3^2+3^3+...+3^{98}\)
\(A=\left(1+3+3^2\right)+.....+\left(3^{97}+3^{98}+3^{99}\right)\) ( Nhóm 3 số 1 nhé )
\(A=13+.....+3^{97}.13⋮13\left(\text{đ}pcm\right)\)
Bài 2 :
Theo ý a ta có :
\(A=13+.....+3^{97}.13+3^{99}+3^{100}\)
\(A=13+.....+3^{97}.13+3^{99}.4⋮̸13\)
Bài 3 :
Để D chia hết cho 2 thì x chia hết cho 2
1. \(A=3^0+3^1+3^2+...+3^{98}\)
\(=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{96}+3^{97}+3^{98}\right)\)
\(=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{96}\left(1+3+3^2\right)\)
\(=13\left(1+3^3+...+3^{96}\right)\)chia hết cho \(13\).
2. \(B=3^0+3^1+3^2+3^3+...+3^{100}\)
\(=1+3+\left(3^2+3^3+3^4\right)+...+\left(3^{98}+3^{99}+3^{100}\right)\)
\(=4+3^2\left(1+3+3^2\right)+...+3^{98}\left(1+3+3^2\right)\)
\(=4+13\left(3^2+3^5+...+3^{98}\right)\)không chia hết cho \(13\).
3. \(D=\left(12.3+26.b+2022.c+x\right)\)chia hết cho \(2\)
\(\Leftrightarrow x⋮2\)(vì \(12.3⋮2,26b⋮2,2022c⋮2\))
\(a,TH1:x-2021=0=>x=2021\)
\(Th2:x-2022=0=>x=2022\)
Vậy \(x\in\left\{2021;2022\right\}\)
\(b,x\left(8-5\right)=1080\)
\(x.3=1080\)
\(x=360\)
\(c,x^3=216< =>6^3=216=>x=3\)
\(d,5^5=3125\)
a) ( x- 2021) * ( x- 2022) = 0
=> \(\orbr{\begin{cases}x-2021=0\\x-2022=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2021\\x=2022\end{cases}}}\)
b) b. 8x - 5x = 2022
=> 3x = 2022
=> x = 674
c) \(5\cdot x^3=1080\)
=> \(x^3=216\)
=> \(x^3=6^3\)
=> x = 6
d) \(5^x=3125\)
=> \(5^x=5^5\)
=> x = 5
a. 100 - 7 ( x - 5 ) = 58
<=> 7 ( x - 5 ) = 100 - 58
<=> 7 ( x - 5 ) = 42
<=> x - 5 = 42 : 7
<=> x - 5 = 6
<=> x = 6 + 5
<=> x = 11
Tương tự tiếp.
a;100-7(x-5)=58
=>7(x-5)=100-58=42
=>x-5=42:7=6
=>x=6+5=11
b;12(x-1):3=72
=>12(x-1)=72.3=216
=>x-1=216:12=18
=>x=18+1=19
c;12-4(x-1)=4
=>4(x-1)=12-4=8
=>x-1=8:4=2
=>x=2+1=3
d;32-12x=8
=>12x=32-8=24
=>x=24:12=2
nho h do nhe viet moi tay lam day biet ko
\(a)\)\(\left(50-6.x\right).18=2^3.3^2.5\)
\(\Leftrightarrow\)\(\left(50-6.x\right).18=8.9.5\)
\(\Leftrightarrow\)\(\left(50-6.x\right).18=360\)
\(\Leftrightarrow\)\(\left(50-6.x\right)=360\div18\)
\(\Leftrightarrow\)\(50-6.x=20\)
\(\Leftrightarrow\)\(6.x=50-20\)
\(\Leftrightarrow\)\(6.x=30\)
\(\Leftrightarrow\)\(x=5\)
\(b)\)\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=7450\)
\(\Leftrightarrow\)\(100x+\left(1+2+3+...+100\right)=7450\)
\(\Leftrightarrow\)\(100x+5050=7450\)
\(\Leftrightarrow\)\(100x=7450-5050\)
\(\Leftrightarrow\)\(100x=2400\)
\(\Leftrightarrow\)\(x=24\)
b.
(x+1)+(x+2)+...+(x+100)=7450
=> 100x + (1+2+3+...+100)=7450
=>100x + (100+1).50=7450
=>100x=2400
=>x=24
a) x2.x3:7=224
=>x5 :7=224
=>x5 =32
=>x5 =25 => x=2
b)x3 :xx +7=8
=>x3-x =1
=>x3-x =13-x
=> x=1
c) xn =1
=> xn=1n
=> x=1
k cho minh nhee:3
\(1.x^2+11x=0\)
\(\Leftrightarrow x\left(x+11\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x+11=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=-11\end{cases}}\)
\(2.\left(x^2-1\right)\left(x^2-9\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-1\right)\left(x+9\right)\left(x-9\right)=0\)
chia thành 4 TH :
\(TH1:X-1=0\)
\(\Leftrightarrow x=1\)
\(TH2:x+1=0\)
\(\Leftrightarrow x=-1\)
\(TH3:X+9=0\)
\(\Leftrightarrow X=-9\)
\(TH4:x-9=0\)
\(\Leftrightarrow x=9\)
Kết luận ....
\(3.\left(\left|x+1\right|-5\right)\left(x^2-9\right)\)
\(\Leftrightarrow\left(\left|x+1\right|-5\right)\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}\left|x+1\right|-5=0\\x-3=0\\x+3=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\left|x+1\right|=5\\x=3\\x=-3\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x+1=+_-5\Leftrightarrow x+1=5,x+1=-5\Leftrightarrow x=4,x=-6\\x=3x\\x=-3\end{cases}}\)
kết luận x=.....
\(4.\left(3x-16\right)⋮\left(x+2\right)\)
\(\Leftrightarrow\left(3x+6\right)-22\)
\(\Leftrightarrow3\left(x+2\right)-22⋮\left(x+2\right)\)
Vì\(\left(x+2\right)⋮\left(x+2\right)\)
\(\Rightarrow\left(3x-16\right)⋮\left(x+2\right)\)
Kết luận x=.....
\(x\ge4\)
k nha