РЕШЕНИЕ
1а) - НЕТ
a² + b² ≠ a² + 2ab + b²
1б) - ДА
(a-b)² + 4ab = a² - 2ab + 4ab = a²+2ab+b² = (a+b)²
2)
(a+2b)² + (a-2b) = a² + 4ab+4b² +a - 2b = 8ab =
= (a-2b)²+(a-2b) = (a-2b)(a-2b+1) =?
2<x<8
a) 2*4 < 4x < 8*4
8 < 4x < 32
б) -8 < -x < -2
-8*8 < -8x < -2*8
-64 < -8x < -16
в) 2-4 < x-4 < 8-4
-2 < x-4 < 4
г) 2*2+4 < 2x+4 < 2*8+4
8 < 2x+4 < 20
1)сosa=-√1-0,36=-0,8
2sinacosa+cos²a-sin²a=2*(-0,8)*(-0,6)+(-0,6)²-(-0,8)²=0,96+0,36-0,64=0,68
2)cosa=√1-0,64=0,6
cos²a-sin²a+6sina/cosa=0,36-0,64+6*(-0,8)/0,6=-0,28-8=-8,28
3)sin(π/4-a)=sinπ/4cosa-cosπ/4sina=√2/2(cosa-sina)=√3/8⇒ cosa-sina=√3/8:1/√2=√3/8*√2=√6/8
(cosa-sina)²=cos²a+sin²a-2cosasina=1-sin2a=(√6/8)²=6/64=3/32⇒
sin2a=1-3/32=29/32
4)cos(a+π/4)=cosacosπ/4-sinasinπ/4=√2/2(cosa-sina)=√5/8⇒ cosa-sina=√5/8:1/√2=√5/8*√2=√10/8
(cosa-sina)²=cos²a+sin²a-2cosasina=1-sin2a=(√10/8)²=10/64=5/32
sin2a=1-5/32=27/32
Q=3:6 = 1/2
b4 = b1*q³ = 6*1/8 = 6/8= 3/4
S5 = b4(q^5-1)/(q-1) =
=3/4*(1/32-1)/(1/2 -1) = 3/4*(-31/32): (-1/2)= 3/4*31/32*2/1)= =93/64
Ответ: 64*S = 64*93/64 = 93