a: =>x=y+11

xy=60

=>y(y+11)=60

\(\Leftrightarrow y^2+15y-4y-60=0\)

=>(y+15)(y-4)=0

hay \(y\in\left\{-15;4\right\}\)

bài 1: 

\(\left\{{}\begin{matrix}x+y=57\\4x-2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+4y=228\\4x-2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6y=234\\x+y=57\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=39\\x=18\end{matrix}\right.\)

a.

\(\Leftrightarrow\dfrac{\sqrt{2}}{2}sin4x+\dfrac{\sqrt{2}}{2}cos4x=\dfrac{\sqrt{6}}{2}\)

\(\Leftrightarrow cos4x.cos\left(\dfrac{\pi}{4}\right)+sin4x.sin\left(\dfrac{\pi}{4}\right)=\dfrac{\sqrt{6}}{2}\)

\(\Leftrightarrow cos\left(4x-\dfrac{\pi}{4}\right)=\dfrac{\sqrt{6}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}4x-\dfrac{\pi}{4}=arccos\left(\dfrac{\sqrt{6}}{2}\right)+k2\pi\\4x-\dfrac{\pi}{4}=-arccos\left(\dfrac{\sqrt{6}}{2}\right)+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{16}+\dfrac{1}{4}arccos\left(\dfrac{\sqrt{6}}{2}\right)+\dfrac{k\pi}{4}\\x=\dfrac{\pi}{16}-\dfrac{1}{4}arccos\left(\dfrac{\sqrt{6}}{2}\right)+\dfrac{k\pi}{4}\end{matrix}\right.\)

b.

\(\Leftrightarrow\dfrac{\sqrt{3}}{2}sinx+\dfrac{1}{2}cosx=\dfrac{\sqrt{3}}{6}\)

\(\Leftrightarrow cosx.cos\left(\dfrac{\pi}{3}\right)+sinx.sin\left(\dfrac{\pi}{3}\right)=\dfrac{\sqrt{3}}{6}\)

\(\Leftrightarrow cos\left(x-\dfrac{\pi}{3}\right)=\dfrac{\sqrt{3}}{6}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{\pi}{3}=arccos\left(\dfrac{\sqrt{3}}{6}\right)+k2\pi\\x-\dfrac{\pi}{3}=-arccos\left(\dfrac{\sqrt{3}}{6}\right)+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+arccos\left(\dfrac{\sqrt{3}}{6}\right)+k2\pi\\x=\dfrac{\pi}{3}-arrcos\left(\dfrac{\sqrt{3}}{6}\right)+k2\pi\end{matrix}\right.\)

c.

\(\Leftrightarrow\dfrac{\sqrt{3}}{2}cosx+\dfrac{1}{2}sinx=-\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow cosx.cos\left(\dfrac{\pi}{6}\right)+sinx.sin\left(\dfrac{\pi}{6}\right)=cos\left(\dfrac{3\pi}{4}\right)\)

\(\Leftrightarrow cos\left(x-\dfrac{\pi}{6}\right)=cos\left(\dfrac{3\pi}{4}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{\pi}{6}=\dfrac{3\pi}{4}+k2\pi\\x-\dfrac{\pi}{6}=-\dfrac{3\pi}{4}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11\pi}{12}+k2\pi\\x=-\dfrac{7\pi}{12}+k2\pi\end{matrix}\right.\)

1 inheritance

2 dental

3 fascinating

4 confidence

5 amazement

6 Surprisingly

7 depressed

8 dissatisfication

9 laziness

10 admiration

1. inheritance 
2. Dental
3. fascinating
4. confidence
5. amazement
6. Surprisingly
7. depressed
8. dissatisfaction
9. laziness
10. admiration