A A

A

A

a-a

Đặt \(\left\{{}\begin{matrix}x+y=a\\xy=b\end{matrix}\right.\)thì hệ trở thành

\(\left\{{}\begin{matrix}a^4=6b^2-215\\b\left(a^2-2b\right)=-78\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(\dfrac{-78}{b}+2b\right)^2=6b^2-215\left(1\right)\\a^2=\dfrac{-78}{b}+2b\left(2\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow2b^4+97b^2-6084=0\)

\(\Leftrightarrow\left[{}\begin{matrix}b=6\\b=-6\end{matrix}\right.\)

Làm nốt nhé

c.

\(\Leftrightarrow cos\left(x+12^0\right)+cos\left(90^0-78^0+x\right)=1\)

\(\Leftrightarrow2cos\left(x+12^0\right)=1\)

\(\Leftrightarrow cos\left(x+12^0\right)=\dfrac{1}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+12^0=60^0+k360^0\\x+12^0=-60^0+k360^0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=48^0+k360^0\\x=-72^0+k360^0\end{matrix}\right.\)

2.

Do \(-1\le sin\left(3x-27^0\right)\le1\) nên pt có nghiệm khi:

\(\left\{{}\begin{matrix}2m^2+m\ge-1\\2m^2+m\le1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2m^2+m+1\ge0\left(luôn-đúng\right)\\2m^2+m-1\le0\end{matrix}\right.\)

\(\Rightarrow-1\le m\le\dfrac{1}{2}\)

a.

\(\Rightarrow\left[{}\begin{matrix}x+15^0=arccos\left(\dfrac{2}{5}\right)+k360^0\\x+15^0=-arccos\left(\dfrac{2}{5}\right)+k360^0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-15^0+arccos\left(\dfrac{2}{5}\right)+k360^0\\x=-15^0-arccos\left(\dfrac{2}{5}\right)+k360^0\end{matrix}\right.\)

b.

\(2x-10^0=arccot\left(4\right)+k180^0\)

\(\Rightarrow x=5^0+\dfrac{1}{2}arccot\left(4\right)+k90^0\)

2.

Phương trình \(sin\left(3x-27^o\right)=2m^2+m\) có nghiệm khi:

\(2m^2+m\in\left[-1;1\right]\)

\(\Leftrightarrow\left\{{}\begin{matrix}2m^2+m\le1\\2m^2+m\ge-1\end{matrix}\right.\)

\(\Leftrightarrow\left(m+1\right)\left(2m-1\right)\le0\)

\(\Leftrightarrow-1\le m\le\dfrac{1}{2}\)

1)  (27-514)-(486-78)

    =-487-408

   =-895

2)=40

3)=407

1. \(\left(27-514\right)-\left(486-78\right)\)

\(=\left(-487\right)-408\)

\(=-895\)

2. \(\left(65-100\right)-\left(25-100\right)\)

\(=\left(-35\right)-\left(-75\right)\)

\(=40\)

3. \(\left(567-67\right)-\left(56+4+33\right)\)

\(=500-93\)

\(=407\)

\(Cau1\left(27-514\right)-\left(486-78\right)\)

\(=\left(-487\right)-408\)

\(=-895\)

\(Cau2:\left(65-100\right)-\left(25-100\right)\)

\(=-35-\left(-75\right)\)

\(=40\)

\(Cau3:\left(567-67\right)-\left(56+4+33\right)\)

\(=500-\left(60+33\right)\)

\(=500-93\)

\(=407\)