Cho dạng toàn phương Q: R4 R xác định bởi\[{\rm{Q(x, y, z, t) = 3}}{{\rm{x}}^{\rm{2}}}{\rm{ + 2}}{{\rm{y}}^{\rm{2}}} - {{\rm{z}}^{\rm{2}}} - {\rm{2}}{{\rm{t}}^{\rm{2}}}{\rm{ + 2xy}} - {\rm{4yz + 2yt}}\]. Tìm chỉ số quán tính dương p và chỉ số quán tính âm q?

A. \[\sqrt 3 + \frac{{\rm{\pi }}}{{\rm{6}}}\]

B. \[\sqrt 3 - \frac{{\rm{\pi }}}{{\rm{6}}}\]

C. \[\frac{{{\rm{5\pi }}}}{{\rm{6}}} - \sqrt 3 \]

D. \[{\rm{\pi }} - 2\]

A. \[{\rm{I}} = 60\frac{2}{7}\]

B. \[{\rm{I}} = 66\frac{2}{7}\]

C. \[{\rm{I}} = - 60\frac{2}{7}\]

D. \[{\rm{I}} = - 66\frac{2}{7}\]

A. \[\frac{{{\rm{xsin(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

B. \[\frac{{ - {\rm{x}}\sin (\sqrt {1 + {{\rm{x}}^2}} )}}{{(\sqrt {1 + {{\rm{x}}^2}} )}}\]

C. \[\frac{{{\rm{2xsin(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

D. \[\frac{{{\rm{xcos(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}{{{\rm{(}}\sqrt {{\rm{1 + }}{{\rm{x}}^{\rm{2}}}} {\rm{)}}}}\]

A. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = \frac{{13}}{4}}\end{array}} \right.\)

B. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = - \frac{{13}}{4}}\end{array}} \right.\)

C. \(\left\{ {\begin{array}{*{20}{c}}{a = - \frac{1}{4}}\\{b = - \frac{3}{4}}\end{array}} \right.\)

D. \(\left\{ {\begin{array}{*{20}{c}}{a = \frac{1}{4}}\\{b = - \frac{3}{4}}\end{array}} \right.\)

A. \[[ - 1; + \infty )\]

B. \[(1; + \infty )\]

C. \[[\frac{{ - 1}}{3}; + \infty )\]

D. \[( - 1; + \infty )\]

A. \[{\rm{I}} = \frac{{{\rm{2\pi }}}}{{\rm{3}}} - \frac{{\sqrt 3 }}{2}\]

B. \[{\rm{I}} = \frac{{{\rm{2\pi }}}}{{\rm{3}}} + \frac{{\sqrt 3 }}{2}\]

C. \[{\rm{I}} = - \frac{{{\rm{2\pi }}}}{{\rm{3}}} - \frac{{\sqrt 3 }}{2}\]

D. \[{\rm{I}} = - \frac{{{\rm{2\pi }}}}{{\rm{3}}} + \frac{{\sqrt 3 }}{2}\]