а) f(x-9) = f(x+5(x-9)^3 = (x+5)^(x-9)(x-9)(x-9) = (x+5)(x+5)(x+5Раскроем скобкиx^3 - 27x^2 + 243x - 729 = x^3 + 15x^2 + 75x + 12Упростим:
b) f(2x-7) = f(2x+3(2x-7)^3 = (2x+3)^(2x-7)(2x-7)(2x-7) = (2x+3)(2x+3)(2x+3Раскроем скобки8x^3 - 56x^2 + 168x - 343 = 8x^3 + 12x^2 + 18x + 2Упростим:
в) f(x-1) = f(x-7(x-1)^3 = (x-7)^(x^3 - 3x^2 + 3x - 1) = (x^3 - 21x^2 + 147x - 343-x^2 + 144x - 342 = 0
г) f(1+3x) = f(3x+5(1+3x)^3 = (3x+5)^(1+3x)(1+3x)(1+3x) = (3x+5)(3x+5)(3x+5Раскроем скобки27x^3 + 27x^2 + 9x + 1 = 27x^3 + 45x^2 + 135x + 12Упростим27x^2 - 108x + 124 = 0
а) f(x-9) = f(x+5
27x^2 + 243x - 729 = 15x^2 + 75x + 12542x^2 + 168x - 854 = 0(x-9)^3 = (x+5)^
(x-9)(x-9)(x-9) = (x+5)(x+5)(x+5
Раскроем скобки
x^3 - 27x^2 + 243x - 729 = x^3 + 15x^2 + 75x + 12
Упростим:
b) f(2x-7) = f(2x+3
56x^2 + 168x - 343 = 12x^2 + 18x + 2768x^2 + 150x - 370 = 0(2x-7)^3 = (2x+3)^
(2x-7)(2x-7)(2x-7) = (2x+3)(2x+3)(2x+3
Раскроем скобки
8x^3 - 56x^2 + 168x - 343 = 8x^3 + 12x^2 + 18x + 2
Упростим:
в) f(x-1) = f(x-7
(x-1)^3 = (x-7)^
(x^3 - 3x^2 + 3x - 1) = (x^3 - 21x^2 + 147x - 343
-x^2 + 144x - 342 = 0
г) f(1+3x) = f(3x+5
(1+3x)^3 = (3x+5)^
(1+3x)(1+3x)(1+3x) = (3x+5)(3x+5)(3x+5
Раскроем скобки
27x^3 + 27x^2 + 9x + 1 = 27x^3 + 45x^2 + 135x + 12
Упростим
27x^2 - 108x + 124 = 0