(x-1)/(2x-1) <1
[(x-1)/(2x-1)] -1<0
[(x-1-2x+1)]/(2x-1)<0
-x/(2x-1) <0
x/(2x-1)>0
____+____(0)____-____(1/2)___+______
x e (-беск.; 0) U (1/2;+беск.)
1a) ax² - 4a = a(x² - 4) = a(x - 2)(x + 2)
б) 3m² - 12m + 12 = 3(m² - 4m + 4) = 3(m - 2)² = 3(m - 2)(m - 2)
в) 5x³ + 5y³ = 5(x³ + y³) = 5(x + y)(x² - xy + y²)
г) z⁴ - x¹² = (z²)² - (x⁶)² = (z² - x⁶)(z² + x⁶) = (z - x³)(z + x³)(z² + x⁶)
2a)6 - 3y + 18x - 9xy = (6 - 3y) + (18x - 9xy) = 3(2 - y) + 9x(2 - y) =
= (2 - y)(3 + 9x) = 3(2 - y)(1 + 3x)
б) a² - 4a + 4 - p² = (a² - 4a + 4) - p² = (a - 2)² - p² = (a - 2 - p)(a - 2 + p)
в) b² + b + c - c² = (b² - c²) + (b + c) = (b - c)(b + c) + (b + c) =
= (b + c)(b - c + 1)
3)3y³ - 12y² = 0
3y²(y - 4) = 0
3 ≠ 0
y² = 0 ⇒ y₁ = 0
y - 4 = 0 ⇒ y₂ = 4
Ответ : 0 ; 4
3)
x^2+y^2=37
xy=6
xy/y=6/y => x=6/y
(6/y)^2+y^2=37
y=-6,6,-1,1
y=-6
x^2+(-6)^2=37
x^2=-36+37
x=+-1
y=6
x=1,-1
y=-1
x^2+(-1)^2=37
x=6,-6
=> (-1;-6)(1;6)(-6;-1)(6;1)
(6а-2)^2=36а^2-24а+4
(5b+6)^2=25b^2+60b+36
(4+2a)^3=64+96a+32a^2+8a^3
(2a-1)^3=8a^3-12a^2+6a-1
А)√0.04*16=0.2*16=3.2
б)289/625==0.4624