Y=x²+3x-5+2-x=x²+2x-3 x∈[0;2)
y`=2x+2=0
2x=-2
x=-1∉[0;2)
y(0)=-3 наим
y=x²+3x-5-2+x=x²+4x-7 x∈[2;5]
y`=2x+4
=0
2x=-4
x=-2∉[2;5]
y(5)=25+20-7=38 наиб
1претендент+2 претендент+3 претендент
1+2+4
2+3+4
Итого - 3 способа
1)1/30
2)3/10
3)7 целых 6/7
4)3 целых 5/8
5)103/24
6)49
7)5/4
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
решение разделено по действиям
m²-2m+4 2m²+m (m²-2m+4) *m*(2m+1) m
-------------* ------------ = ------------------------------------------------ = ----------------
4m²-1 m³+8 (2m-1)(2m+1)*(m+2)*(m²-2m+4) (2m-1)(m+2)
------------------------------------------------------------------------------------------------------
m m+2 m m+2
------------------ - ------------- = ------------------ - --------------------- =
(2m-1)(m+2) 2m²- m (2m-1)(m+2) m*(2m-1)
m *m - (m+2)(m+2) m²-(m+2)²
---------------------------------------- = --------------------------- =
(2m-1)*(m+2) *m (2m-1)*(m+2)*m
m²- (m²+2m+4) m²- m²- 2m-4 -2(m+2) -2
--------------------------- = ------------------------- = ------------------------- = ------------
(2m-1)*(m+2)*m (2m-1)*(m+2)*m (2m-1)*(m+2)*m (2m-1)m
------------------------------------------------------------------------------------------------------
-2 4 -2 *m(m+2) -(m+2)
------------- : ------------ = --------------------- = ------------------
(2m-1)m m²+2m (2m-1)m *4 (2m-1)*2
---------------------------------------------------------------------------------------------------
-(m+2) 10m+1 -(m+2) 10m+1
----------------- - --------------- = -------------- + ------------- =
(2m-1)*2 4-8m (2m-1)*2 8m- 4
-(m+2) 10m+1 - 2*(m+2)+10m+1
--------------+ ------------------- = ---------------------------- =
(2m-1)*2 4* (2m-1) 4* (2m-1)
-2m -4+10m+1 8m- 3
----------------------- = ---------------
4* (2m-1) 4* (2m-1)