По теореме Виета х₁+х₂=5, а по условию х₁-х₂=3
Получаем систему
х₁+х₂=5
х₁-х₂=3
Складываем почленно уравнение и получаем 2х₁=8
х₁=4
х₂=1
Произведение равно 4, ответ: а = 4
Функция <em>sin t </em>нечетная: <em>sin</em>(-<em>t</em>) = - <em>sin t, </em>
функция<em> </em><em>cos t </em>четная: <em>cos</em>(-<em>t</em>) = <em>cos t</em>;
функции <em>sin t </em>и <em>cos t - </em>периодические, 2<span><span /></span> - основной период:
<span><span><span>sin</span><span>(</span><span>t</span><span /><span><span>2</span></span><span>k</span><span>)</span><span><span>=</span></span><span><span>s</span></span><span>int</span></span></span> и <span><span><span>cos</span><span>(</span><span>t</span><span /><span><span>2</span></span><span>k</span><span>)</span><span><span>=</span></span><span><span>c</span></span><span>ost</span></span></span>, где <em>k</em> - любое целое число;
область значений функций <em>sin t </em>и <em>cos t - </em>отрезок [ -1; 1];
функция <em>y</em> = <em>sin t </em>возрастает на промежутках <span><span><span><span><span /><span>−</span><span><span><span>2</span></span></span><span><span /></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span><span><span>2</span></span></span><span><span /></span></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>
и убывает на промежутках <span><span><span><span><span /><span><span><span>2</span></span></span><span><span /></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span><span><span>2</span></span></span><span><span><span>3</span></span><span /></span></span><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>, <span><span><span>k</span><span /><span><span>Z</span></span></span></span>;
функция <em>y</em> = <em>cos t </em>убывает на промежутках <span><span><span><span><span /><span>2</span><span>k</span><span>;</span><span /><span><span>+</span></span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>
и возрастает на промежутках <span><span><span><span><span /><span>−</span><span><span>+</span></span><span><span>2</span></span><span>k</span><span>;</span><span><span>2</span></span><span>k</span><span /> </span></span></span></span>, <span><span><span>k</span><span /><span><span>Z</span></span></span></span>.
(2а-3в)(4а2-6ав+9в2)-8а3+27в3=
