Решение:
(2x+5)² - (2x-3)(2x+1)=4
4х²+20х+25-(4х²+2х-6х-3)=4
4х²+20х+25-4х²-2х+6х+3-4=0
24х+24=0
24х=-24
х=-
=-1
х=-1
Проверка:
(2×(-1)+5)² - (2×(-1)-3)(2(-1)+1)=4
(-2+5)²-(-2-3)(-2+1)=4
3²-(-5)×(-1)=4
9-5=4
4=4
Ответ: х=-1.
64⁻¹32²=(2⁶)⁻¹(2⁵)²=2⁻⁶2¹⁰=2⁻⁶⁺¹⁰=2⁴=16
(6³)²:36⁵=6⁶:(6²)⁵=6⁶:6¹⁰=6⁶⁻¹⁰=6⁻⁴=1/1296
(4⁻³2⁵)/8⁻⁴=2⁻⁶2⁵/2⁻¹²=2⁻⁶⁺⁵⁻⁽⁻¹²⁾=2¹¹=2048
(3⁻³)³3⁷/27²=3⁻⁹3⁷/3⁶=3⁻⁹⁺⁷⁻⁶=3⁻⁸=1/6561
<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
Это бесконечно убывающая геометрическая прогрессия. Первый член
и знаменателем
Тогда сумма:
Y=5cosx+8x-3
y`=-5sinx+8=0
sinx=1,6>1 нет корней
y(-3π/2)=5cos(-3π/2)+8*(-3π/2)-3≈-40,69
y(0)=5cos0+8*0-3=2 наиб
