1) 64m^3 -1 = (4m)^3 - 1^3 = (4m - 1)*(16m^2 + 4m + 1)
2) (x-3)*(x^2 +3x +9) - x(x^2 -16) = 21
x^3 - 3^3 - x^3 + 16x^2 = 21
16x^2 = 21 + 27
16x^2 = 48
x^2 = 3
x_1 = -V3, x_2 = V3
3) (a+3)^3 - (a-1)^3 - 12a^3 = a^3 + 3a^2*3 + 3a*9 + 27 - a^3 + 3a^2 * 1 - 3a*1 + 1 -
-12a^3 = -12a^3 + 12a^2 + 24a + 28 = -4(a^3 - 3a^2 - 6a - 7)
4) (x+2)^3 - x(3x+1)^2 + (2x+1)(4x^2 -2x+1) = 42
x^3 + 3x^2 *2 + 3x*2^2 + 2^3 - 9x^3 - 6x^2 - x + (2x)^3 + 1^3 -42 = 0
11x = 33
x = 3
5) (x^n + x^(n-1))^3 = x^3n + 3x^2n *x^(n-1) + 3x^n *(x^(n-1))^2 + (x^(n-1))^3 =
= x^3n + 3x^(3n-1) + 3x^(3n -2) + x^(3n-3) = x^3n(1 + 3x^(-1) + 3x^(-2) + x^(-3))
6) (a-1)^3 + 3(a-1)^2 + 3(a-1) + 1 + a^3 = a^3 - 3(a-1)^2 + 3(a-1) - 1 +3(a-1)^2 +
+3(a-1) + 1+ a^3 = 2a^3 + 6(a-1) + 1 = 2a^3 + 6a - 5
1) 64m^3 -1 = (4m)^3 - 1^3 = (4m - 1)*(16m^2 + 4m + 1)
2) (x-3)*(x^2 +3x +9) - x(x^2 -16) = 21
x^3 - 3^3 - x^3 + 16x^2 = 21
16x^2 = 21 + 27
16x^2 = 48
x^2 = 3
x_1 = -V3, x_2 = V3
3) (a+3)^3 - (a-1)^3 - 12a^3 = a^3 + 3a^2*3 + 3a*9 + 27 - a^3 + 3a^2 * 1 - 3a*1 + 1 -
-12a^3 = -12a^3 + 12a^2 + 24a + 28 = -4(a^3 - 3a^2 - 6a - 7)
4) (x+2)^3 - x(3x+1)^2 + (2x+1)(4x^2 -2x+1) = 42
x^3 + 3x^2 *2 + 3x*2^2 + 2^3 - 9x^3 - 6x^2 - x + (2x)^3 + 1^3 -42 = 0
11x = 33
x = 3
5) (x^n + x^(n-1))^3 = x^3n + 3x^2n *x^(n-1) + 3x^n *(x^(n-1))^2 + (x^(n-1))^3 =
= x^3n + 3x^(3n-1) + 3x^(3n -2) + x^(3n-3) = x^3n(1 + 3x^(-1) + 3x^(-2) + x^(-3))
6) (a-1)^3 + 3(a-1)^2 + 3(a-1) + 1 + a^3 = a^3 - 3(a-1)^2 + 3(a-1) - 1 +3(a-1)^2 +
+3(a-1) + 1+ a^3 = 2a^3 + 6(a-1) + 1 = 2a^3 + 6a - 5
А) (х-1)(х-3)≥0
x=1 x=3
x∈(-∞;1] U [3;∞)
Б)х(2-х)<0
x=0 x=2
x∈(-∞;0) U (2;∞)
Решите неравенство:
А) х²-4х+3≥0
x1+x2=4 U x1*x2=3⇒x1=1 U x2=3
x∈(-∞;1} U {3;∞)
Б)х(х²-9)<0
x(x-3)(x+3)<0
x=0 x=3 x=-3
_ + _ +
(-3)(0)(3)
x∈(-∞;-3) U (1;3)
Решите неравенство: (3х+1)/(2-х) <2
(3x+1)/(2-x)-2<0
(3x+1-4+2x)/(2-x)<0
(5x-3)/(2-x)<0
x=0,6 x=2
x∈(-∞;0,6) U (2;∞)
Найдите область определения функции:
А)у=√(3-х)
3-x≥0⇒x≤3
D(y)∈(-∞;3]
Б)у = 2/(х² -9)
x²-9≠0
x²≠9
x≠3
x≠-3
D(y)∈(-∞;-3) U (-3;3) U (3;∞)