Tìm các số nguyên dương x,y thỏa mãn : 11x+18y= 120
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1. Bằng mồm
2. bà đi tàu ngầm
3. Hổ chết là hết chỗ
4. CẤM ĐĂNG LINH TINH
5. HẾT
1. If it hadn't been for the awful weather, we wouldn't have cancelled our picnic.
2.1. In order to catch the train, he ran to the station
2.2. He ran to the station so as to catch the train.
3. So as to listen to the football news, the boy turned the radio.
4. In order not to wake up her baby, mother entered the room quietly.
5. To earn some extra money, he plays the guitar for a small group.
a) \(\sqrt{1-x}=\sqrt[3]{8}\) ( ĐK: \(x\le1\) )
\(\Leftrightarrow\sqrt{1-x}=2\)
\(\Leftrightarrow1-x=4\)
\(\Leftrightarrow x=-3\) ( Thỏa mãn )
b) \(\sqrt{4x^2-12x+9}=x+1\) ( ĐK : \(x\ge-1\) )
\(\Leftrightarrow\sqrt{\left(2x\right)^2-2.2x.3+3^2}=x+1\)
\(\Leftrightarrow\sqrt{\left(2x-3\right)^2}=x+1\)
\(\Leftrightarrow\left|2x-3\right|=x+1\)
\(\Leftrightarrow\orbr{\begin{cases}2x-3=x+1\\3-2x=x+1\end{cases}}\) \(\Leftrightarrow\orbr{\begin{cases}x=4\\x=\frac{2}{3}\end{cases}}\) ( Thỏa mãn )
c) \(x+\sqrt{x}-2=0\) ( ĐK : \(x\ge0\) )
\(\Leftrightarrow\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)=0\)
\(\Leftrightarrow\sqrt{x}-1=0\)
\(\Leftrightarrow x=1\) ( Thỏa mãn )
+) ĐKXĐ : \(x\le1\)
\(\sqrt{1-x}=\sqrt[3]{8}\)
\(\Leftrightarrow\sqrt{1-x}=2\)
\(\Leftrightarrow1-x=4\)
\(\Leftrightarrow x=-3\left(TM\right)\)
+) \(\sqrt{4x^2-12x+9}=x+1\)
\(\Leftrightarrow\sqrt{\left(2x-3\right)^2}=x+1\)
\(\Leftrightarrow\left|2x-3\right|=x+1\)
\(\Leftrightarrow\orbr{\begin{cases}2x-3=x+1\left(x\ge\frac{3}{2}\right)\\2x-3=-x-1\left(x< \frac{3}{2}\right)\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-x=3+1\\2x+x=3-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=4\\3x=2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=4\\x=\frac{2}{3}\end{cases}\left(TM\right)}}\)
+) ĐKXĐ : \(x\ge0\)
\(x+\sqrt{x}-2=0\)
\(\Leftrightarrow\sqrt{x}\left(\sqrt{x}+1\right)=2\)
+) \(\hept{\begin{cases}\sqrt{x}=1\\\sqrt{x}+1=2\end{cases}\Leftrightarrow\hept{\begin{cases}x=1\\x=1\end{cases}\Leftrightarrow}x=1\left(TM\right)}\)
+) \(\hept{\begin{cases}\sqrt{x}=2\\\sqrt{x}+1=1\end{cases}\Leftrightarrow\hept{\begin{cases}x=\sqrt{2}\\x=0\end{cases}}}\left(TM\right)\)
Gọi số cần tìm là ab
Ta có 5 x ab = 3ab
=> 5 x ab = 300 + ab
=> 4 x ab = 300
=> ab = 75
Vậy số cần tim là 375
Bài làm:
1) \(3\sqrt{12}-4\sqrt{27}+5\sqrt{48}\)
\(=3.2\sqrt{3}-4.3\sqrt{3}+5.4\sqrt{3}\)
\(=6\sqrt{3}-12\sqrt{3}+20\sqrt{3}\)
\(=14\sqrt{3}\)
2) \(\left(\sqrt{45}-2\sqrt{10}+\sqrt{5}\right).\sqrt{5}+5\sqrt{8}\)
\(=3\sqrt{5}.\sqrt{5}-2\sqrt{10}.\sqrt{5}+\sqrt{5}.\sqrt{5}+5.2\sqrt{2}\)
\(=15-10\sqrt{2}+5+10\sqrt{2}\)
\(=20\)
\(2\sin2x-\cos2x=7\sin x+2\cos x-4\)
\(\Rightarrow4\sin x\cos x-\left(1-2\sin^2x\right)-7\sin x-2\cos x+4=0\)
\(\Rightarrow2\cos x\left(2\sin x-1\right)+\left(2\sin^2-7\sin x+3\right)=0\)
\(\Rightarrow2\cos x\left(2\sin x-1\right)+\left(2\sin x-1\right)\left(\sin x-3\right)=0\)
\(\Rightarrow\left(2\sin x-1\right)\left(2\cos x+\sin x-3\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2\sin x-1=0\\2\cos x+\sin x=3,\left(vn\right)\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{\eta}{6}+k2\eta\\x=\frac{5\eta}{6}+k2\eta\end{cases}}}\)
\(\eta=Pi;3.14159\)
\(11x+18y=120\)
Có: \(18y⋮6,120⋮6\Rightarrow11x⋮6\Rightarrow x⋮6\)
Đặt \(x=6k\), ta được: \(11k+3y=20\Rightarrow y=\frac{20-11k}{3}=7-4k+\frac{k-1}{3}\)
Đặt \(\frac{k-1}{3}=t\left(t\inℤ\right)\Rightarrow k=3t+1\)
\(\Rightarrow\hept{\begin{cases}y=7-4\left(3t+1\right)=3-11t\\x=6k=18t+6\end{cases}}\)
=>Các nghiệm nguyên của phương trình là :
\(\hept{\begin{cases}x=18t+6\\y=3-116\end{cases}\left(t\inℤ\right)t\text{ùy}}\text{ý}\)