Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 1271

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\[\sin^{2}x - \sin x\cos x -\]

\[- 2\cos^{2}x = a\]

\[(1 - a)\sin^{2}x - \sin x\cos x -\]

\[- (2 + a)\cos^{2}x = 0\]

\[(1 - a)tg^{2}x - tgx -\]

\[- (2 + a) = 0\]

\[Пусть\ tg\ x = y:\]

\[(1 - a)y^{2} - y - (2 + a) = 0\]

\[D = 1 + 4 \cdot (1 - a)(2 + a) =\]

\[= 1 + 4 \cdot \left( 2 - 2a + a - a^{2} \right) =\]

\[= 1 + 8 - 8a + 4a - 4a^{2} =\]

\[= - 4a^{2} - 4a + 9\]

\[- 4a^{2} - 4a + 9 < 0\]

\[4a^{2} + 4a - 9 > 0\]

\[D_{1} = 4 + 36 = 40\]

\[a_{1,2} = \frac{- 2 \pm 2\sqrt{10}}{4} = \frac{- 1 \pm \sqrt{10}}{2}.\]

\[a < \frac{- 1 - \sqrt{10}}{2};\ \ \ a > \frac{- 1 + \sqrt{10}}{2}.\]