Question

(х-3)^3-(x-5)^2(x+1)+4=0

Answer 1

(x-3)³-(x-5)²(x+1)+4=0

раскрываем скобки по формулам (a-b)²=a²-2ab+b²

(a-b)³=a³-3ba²+3ab²-b³

x³-9x²+27x-27-(x²-10x+25)(x+1)+4=0

перемножаем множители

x³-9x²+27x-27-x³+10x²-25x-x²+10x-25+4=0

x³-x³-9x²+10x²-x²+27x+10x-25x-27-25+4=0

12x-48=0

12x=48

x=4

ответ: 4

Answer 2

X^3-9x^2+27x-27-x^3+9x^2-15x-25+4=0
12x-48=0
12x=48
x=4

Answer 3

To solve the equation (х-3)^3 - (x-5)^2(x+1) + 4 = 0, follow these steps:

Step 1: Expand the expressions: (х-3)^3 = (x-3)(x-3)(x-3) = (x^2 - 6x + 9)(x - 3) = x^3 - 6x^2 + 9x - 27 (x-5)^2 = (x-5)(x-5) = (x^2 - 10x + 25) (x-5)^2(x+1) = (x^2 - 10x + 25)(x + 1) = x^3 - 9x^2 + 15x + 25 So the equation becomes: x^3 - 6x^2 + 9x - 27 - (x^3 - 9x^2 + 15x + 25) + 4 = 0

Step 2: Combine like terms: x^3 - 6x^2 + 9x - 27 - x^3 + 9x^2 - 15x - 25 + 4 = 0

Step 3: Simplify the equation: (-6x^2 + 9x^2) + (9x - 15x) + (-27 - 25 + 4) = 0 3x^2 - 6x - 48 = 0

Step 4: Factor the quadratic equation: 3x^2 - 6x - 48 = 3(x^2 - 2x - 16) = 3(x - 8)(x + 2) = 0

Step 5: Set each factor to zero and solve for x: a) x - 8 = 0 --> x = 8 b) x + 2 = 0 --> x = -2

So the solutions to the equation are x = 8 and x = -2.