79067 The sum of the real roots of the equation \(\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0\), is equal to

79068 Let \(m\) and \(M\) be respectively the minimum and
maximum values
\(\begin{array}{ccc} \cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x \end{array}\)
Then, the ordered pair \((\mathrm{m}, \mathrm{M})\) is equal to

79069 Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) If \(B=A+\) \(A^{4}\), then \(\operatorname{det}(B)\)

79070 If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+\)
\(C x+D\), then \(B+C\) is equal to

79071 The maximum value of
\(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right| x \in R \text { is }\)

79067 The sum of the real roots of the equation \(\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0\), is equal to

79068 Let \(m\) and \(M\) be respectively the minimum and
maximum values
\(\begin{array}{ccc} \cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x \end{array}\)
Then, the ordered pair \((\mathrm{m}, \mathrm{M})\) is equal to

79069 Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) If \(B=A+\) \(A^{4}\), then \(\operatorname{det}(B)\)

79070 If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+\)
\(C x+D\), then \(B+C\) is equal to

79071 The maximum value of
\(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right| x \in R \text { is }\)

79067 The sum of the real roots of the equation \(\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0\), is equal to

79068 Let \(m\) and \(M\) be respectively the minimum and
maximum values
\(\begin{array}{ccc} \cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x \end{array}\)
Then, the ordered pair \((\mathrm{m}, \mathrm{M})\) is equal to

79069 Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) If \(B=A+\) \(A^{4}\), then \(\operatorname{det}(B)\)

79070 If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+\)
\(C x+D\), then \(B+C\) is equal to

79071 The maximum value of
\(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right| x \in R \text { is }\)

79067 The sum of the real roots of the equation \(\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0\), is equal to

79068 Let \(m\) and \(M\) be respectively the minimum and
maximum values
\(\begin{array}{ccc} \cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x \end{array}\)
Then, the ordered pair \((\mathrm{m}, \mathrm{M})\) is equal to

79069 Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) If \(B=A+\) \(A^{4}\), then \(\operatorname{det}(B)\)

79070 If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+\)
\(C x+D\), then \(B+C\) is equal to

79071 The maximum value of
\(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right| x \in R \text { is }\)

79067 The sum of the real roots of the equation \(\left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & x+2\end{array}\right|=0\), is equal to

79068 Let \(m\) and \(M\) be respectively the minimum and
maximum values
\(\begin{array}{ccc} \cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x \end{array}\)
Then, the ordered pair \((\mathrm{m}, \mathrm{M})\) is equal to

79069 Let \(\theta=\frac{\pi}{5}\) and \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) If \(B=A+\) \(A^{4}\), then \(\operatorname{det}(B)\)

79070 If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=A x^{3}+B x^{2}+\)
\(C x+D\), then \(B+C\) is equal to

79071 The maximum value of
\(f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right| x \in R \text { is }\)