1) x^2 - 2x + 1 = (x - 1)(x - 1)
2) x^2 + 6x + 9 = (x + 3)(x + 3)
3) x^2 - 25 = x^2 - 5^2 = (x - 5)(x + 5)
4) 27a^3 + 8 = (3a)^3 + 2^3 = (3a + 2)(9a^2 - 6a + 4)
5) 16x^4 - 81 = (4x^2)^2 - (9)^2 = (4x^2 - 9)(4x^2 + 9) =
= (2x - 3)(2x + 3)(4x^2 + 9)
1 + 2cos3xcosx - cos2x = 0
2cos3xcosx = 2(cos(3x+x) +cos(3x-x))/2= cos4x+cos2x
1+cos4x+cos2x-cos2x=0
1+cos4x=0
cos4x=-1
4x = пи +2пи*n
x =пи/4+ (пи/2)*n
Iog2(x²+4x+3)=3
x²+4x+3>0
x²+4x+3=2³
x²+4x+3=8
x²+4x-5=0
D=4²+4*5=16+20=36
√D=6
x1=(-4-6)/2=-5
x2=(-4+6)/2=1
A) 4√5 и 2√6
√(16*5) √(4*6)
√80 √24
√80 > √24
4√5 > 2√6
б) (2√3 + √6)² -18 и (3√2 -2)(4√2 +7)-10
4*3+4√3*√6 +6-18 и 12*2-8√2+21√2-14-10
12+6-18+4√18 и 24-14-10+13√2
4√(9*2) и 13√2
4*3√2 и 13√2
12√2 и 13√2
12√2 < 13√2
(2√3 +√6)²-18 < (3√2 -2)(4√2 +7)-10
(sin(270-36)+cos(180+36))/(sin(180-36)-cos(90+36)) *tg36=
=(-cos36-cos36)/(sin36+sin36 *tg36=-2cos36/2sin36 *tg36=ctg36*tg36=1