А) 2sin2 х - √3sin2 х =0
sin2x=0
2x=пn
x=пn/2
n целое
б) п, 2п и 3п
<span><span>(<span><span>a2</span>−<span>b2</span>+ab−2</span>)</span><span>(<span><span>a2</span>−<span>b2</span>−ab−2</span>)</span>−<span><span>(<span><span>a2</span>−<span>b2</span>−2</span>)</span>2</span>=</span>Возведение в степень:<span><span>(<span><span>a2</span>−<span>b2</span>+ab−2</span>)</span><span>(<span><span>a2</span>−<span>b2</span>−ab−2</span>)</span>−<span>(<span><span>a4</span>−2<span>a2</span><span>b2</span>−4<span>a2</span>+<span>b4</span>+4<span>b2</span>+4</span>)</span>=</span>Раскрытие скобок:<span><span><span>a4</span>+<span>a2</span><span>(<span>−1</span>)</span><span>b2</span>+<span>a3</span><span>(<span>−1</span>)</span>b+<span>a2</span><span>(<span>−2</span>)</span>−<span>b2</span><span>a2</span>+<span>b4</span>+<span>b3</span>a+2<span>b2</span>+<span>a3</span>b+a<span>b3</span><span>(<span>−1</span>)</span></span><span>+<span>a2</span><span>b2</span><span>(<span>−1</span>)</span>+ab<span>(<span>−2</span>)</span>−2<span>a2</span>+2<span>b2</span>+2ab+4−<span>a4</span>+2<span>a2</span><span>b2</span>+4<span>a2</span>−<span>b4</span>−4<span>b2</span>−4=</span></span><span><span>a2</span><span>(<span>−1</span>)</span><span>b2</span>−<span>b2</span><span>a2</span>+<span>b3</span>a+a<span>b3</span><span>(<span>−1</span>)</span>+<span>a2</span><span>b2</span>=</span><span>−<span>a2</span><span>b2</span>−<span>b2</span><span>a2</span>+<span>b3</span>a−a<span>b3</span>+<span>a2</span><span>b2</span>=</span>−a2b2
a^6 + 1/a^4 + 2/a >= 4
a^6 + 1/a^4 + 2/a - 4 >=0
попробуем слева сделать квадрат или сумму квадратов, тогда докажем неравенство
поделим на а, так так a>0
a^5 + 1/a^5 + 2/a^2 - 4/a >=0
a^5 + 1/a^5 - 2*1/a^5*a^5 + 2 - 2 + 2*(1/a^2 - 2*1*1/a + 1) = (√a⁵ - 1/√a⁵)² + 2(1/a - 1)² = (√a⁵ - 1/√a⁵)² + (1/a - 1)² + (1/a -1)² ≥ 0
слева стоит сумму трех квадратов - значит слева выражение больше равна 0 всегда
(√5+4)²-2√5(√5+4)+1=5+8√5+16-10-8√5+1=12