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a)23+3 𝑥 =125 | b) 70 – 5.(𝑥 - 3)= 45 | c) 20 + 5 𝑥 = 57:55
3 𝑥 +23=125 | 70−5 𝑥 +15=45 | 5 𝑥 +20=5755
𝑥=34 | 𝑥=8 | 𝑥=−104
275
a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a, \(x,y\in Z\Rightarrow\left\{{}\begin{matrix}x-3,2y-6\in Z\\x-3,2y-6\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\end{matrix}\right.\)
Ta có bảng:
x-3 | -1 | -5 | 1 | 5 |
2y-6 | -5 | -1 | 5 | 1 |
x | 2 | -2 | 4 | 8 |
y | \(\dfrac{1}{2}\left(loại\right)\) | \(\dfrac{5}{2}\left(loại\right)\) | \(\dfrac{11}{2}\left(loại\right)\) | \(\dfrac{7}{2}\left(loại\right)\) |
Vậy không có x,y thỏa mãn đề bài
b, tương tự câu a
\(c,xy-5x+2y=7\\ \Rightarrow x\left(y-5\right)+2y-10=-3\\ \Rightarrow x\left(y-5\right)+2\left(y-5\right)=-3\\ \Rightarrow\left(x+2\right)\left(y-5\right)=-3\)
Rồi làm tương tự câu a
\(d,xy-3x-4y=5\\ \Rightarrow x\left(y-3\right)-4y+12=17\\ \Rightarrow x\left(y-3\right)-4\left(y-3\right)=17\\ \Rightarrow\left(x-4\right)\left(y-3\right)=17\)
Rồi làm tương tự câu a
B3 a) x=4 b) x=-7 c) x=5 d) x=4
B2 a) -3+ -2+ -1+0+1+2+3+4=4
b) -6+ -5+ -4+ -3+ -2+ -1+0+1+2+3+4=-11
c) -18+-17+-16+-15+-14+-13+-12+-11+-10+-9+-8+-7+-6+-5+-4+3+-2+-1+0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19=19
`#3107.101107`
a,
`2x + 3x = 5^7 \div 5^5`
$\Rightarrow (2 + 3)x = 5^{7 - 5}$
$\Rightarrow 5x = 5^2$
$\Rightarrow 5x = 25$
$\Rightarrow x = 25 \div 5$
$\Rightarrow x = 5$
Vậy, `x = 5`
b,
`5(7x - 45) = 2^3 . 5^2 - 3^2 . 20`
`\Rightarrow 5(7x - 45) = 8.25 - 9.20`
`\Rightarrow 5(7x - 45) = 40.5 - 36.5`
`\Rightarrow 5(7x - 45) = 5.(40 - 36)`
`\Rightarrow 5(7x - 45) = 5.4`
`\Rightarrow 7x - 45 = 4`
`\Rightarrow 7x = 49`
`\Rightarrow x = 49 \div 7`
`\Rightarrow x = 7`
Vậy, `x = 7.`
A) (2+3).x=5 mũ 2
5.x=5 mũ 2
5.x=25
x=25:5
x=5
vậy x=5
câu B ko bt làm bn ạ
\(\left\{-3x+2\left[45-x-3\left(3x+7\right)-2x\right]+4x\right\}=55-103\)
\(\left\{-3x+2\left[45-x-9x-21-2x\right]+4x\right\}=-48\)
\(-3x+90-2x-18x-42-4x+4x=-48\)
\(-3x-2x-18x-4x+4x=-48-90+42\)
\(-23x=-96\Leftrightarrow x=\frac{96}{23}\)
đag rảnh nên ... lm nốt
\(-57:\left[-2\left(2x+1\right)^2-\left(-9\right)^0\right]=-106\)
\(-2\left(2x+1\right)^2+1=57\)
\(-2\left(2x+1\right)^2=56\)
\(\left(2x+1\right)^2=-28\)
\(\Rightarrow\orbr{\begin{cases}2x+1=-2\sqrt{7}\\2x+1=2\sqrt{7}\end{cases}\Rightarrow\orbr{\begin{cases}2x=-1-2\sqrt{7}\\2x=-1+2\sqrt{7}\end{cases}}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{-1-2\sqrt{7}}{2}\\x=\frac{-1+2\sqrt{7}}{2}\end{cases}}\)
Câu 3:
a: 12-15=-3
b: -4+22=18
c: =16-9x(34-25)=16-9x9=16-81=-65
Câu 2:
a: \(x\in\left\{-20;-19;...;19;20\right\}\)
tổng là 0
b: \(x\in\left\{1;2;3;...;29\right\}\)
Số số hạng là 29-1+1=29(số)
Tổng là 15x29=435
giải giúp với lẹ dc ko