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Câu 1:
1: \(\overrightarrow{OM}=\dfrac{\overrightarrow{OA}+\overrightarrow{OD}}{2}=\dfrac{\overrightarrow{BO}+\overrightarrow{OA}}{2}=\dfrac{\overrightarrow{BA}}{2}=-\dfrac{1}{2}\overrightarrow{AB}\)
\(\Leftrightarrow x=-\dfrac{1}{2}\)
\(\overrightarrow{BD}=2\cdot\overrightarrow{BO}=-2\cdot\overrightarrow{OB}\)
nên y=-2
2: \(2\cdot\overrightarrow{ON}=\overrightarrow{OB}+\overrightarrow{OC}=\overrightarrow{DO}+\overrightarrow{OC}=\overrightarrow{DC}=\overrightarrow{AB}\)
Vậy: Các vecto u thỏa mãn là vecto DC và vecto AB
Câu 1:
1: \(\overrightarrow{OM}=\dfrac{\overrightarrow{OA}+\overrightarrow{OD}}{2}=\dfrac{\overrightarrow{BO}+\overrightarrow{OA}}{2}=\dfrac{\overrightarrow{BA}}{2}=-\dfrac{1}{2}\overrightarrow{AB}\)
\(\Leftrightarrow x=-\dfrac{1}{2}\)
\(\overrightarrow{BD}=2\cdot\overrightarrow{BO}=-2\cdot\overrightarrow{OB}\)
nên y=-2
2: \(2\cdot\overrightarrow{ON}=\overrightarrow{OB}+\overrightarrow{OC}=\overrightarrow{DO}+\overrightarrow{OC}=\overrightarrow{DC}=\overrightarrow{AB}\)
Vậy: Các vecto u thỏa mãn là vecto DC và vecto AB
\(B=2+2^2+2^3+2^4+...+2^{99}+2^{100}=2\left(1+2^2+2^3+2^4\right)+...+2^{96}\left(1+2^2+2^3+2^4\right)=2.31+2^6.31+...+2^{96}.31=31\left(2+2^6+...+2^{96}\right)⋮31\)
a) A = (3.4.2¹⁶)² = 3².4².2³²
= 3².(2²)².2³² = 2⁴.2³².3²
= 2³⁶.3²
B = 11.2¹³.4¹¹ - 16⁹
= 11.2¹³.(2²)¹¹ - (2⁴)⁹
= 11.2¹³.2²² - 2³⁶
= 11.2³⁵ - 2³⁶
= 2³⁵.(11 - 2)
= 2³⁵.9
= 2³⁵.3²
b) ƯCLN(A; B) = 2³⁵.3²
c) P = A/B = (2³⁶.3²)/(2³⁵.3²) = 2
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a. Chu vi là \(\left(12+5\right).2=34\left(m\right)\)
Diện tích là \(12.5=60\left(m^2\right)=600000\left(cm^2\right)\)
b. Cần lát \(600000:\left(40.40\right)=375\) viên gạch
a) đkxđ: \(x\ne\pm2\)
Ta có: \(\frac{x+2}{x-2}-\frac{x-2}{x+2}=\frac{4}{x^2-4}\)
\(\Leftrightarrow\frac{\left(x+2\right)^2-\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\frac{4}{\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow8x=4\)\(\Rightarrow x=\frac{1}{2}\)
b) đkxđ: \(x\ne\left\{1;-3\right\}\)
PT \(\Leftrightarrow\frac{\left(x+1\right)\left(x+3\right)-\left(x+2\right)\left(x-1\right)+4}{\left(x-1\right)\left(x+3\right)}=0\)
\(\Rightarrow x^2+4x+3-x^2-x+2+4=0\)
\(\Leftrightarrow3x+10=0\Rightarrow x=-\frac{10}{3}\)
c) đkxđ: \(x\ne\left\{0;-1\right\}\)
\(PT\Leftrightarrow\frac{\left(x-1\right)\left(x+1\right)+1-2x}{x\left(x+1\right)}=\frac{x}{x\left(x+1\right)}\)
\(\Rightarrow x^2-1+1-2x=x\)
\(\Leftrightarrow x^2-3x=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\left(ktm\right)\\x=3\left(tm\right)\end{cases}}\)
d) đkxđ: \(x\ne\left\{1;5\right\}\)
\(PT\Leftrightarrow\frac{x-1-3}{\left(x-1\right)\left(x-5\right)}=\frac{5\left(x-5\right)}{\left(x-1\right)\left(x-5\right)}\)
\(\Rightarrow x-4=5x-25\)
\(\Leftrightarrow4x=21\Rightarrow x=\frac{21}{4}\)
e) đkxđ: \(x\ne\left\{0;-2;2\right\}\)
\(PT\Leftrightarrow\frac{-2x+x+2}{x\left(x-2\right)\left(x+2\right)}=\frac{\left(x-4\right)\left(x-2\right)}{x\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow-x+2=x^2-6x+8\)
\(\Leftrightarrow x^2-5x+6=0\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\Rightarrow\orbr{\begin{cases}x=2\\x=3\end{cases}}\)