Question

Решение уравнение: x3-7x2+12x=0 СРОЧНО!

Answer 1

x³-7x²+12x=0
x(x²-7x+12) = 0
x = 0 или x² - 7x + 12 = 0
D = b² - 4ac = 49-4*12 = 49 - 48 = 1
D>0 ⇒ уравнение имеет 2 корня 
x1 = (-b+√D)/2a=(7+1)/2 = 8/2 = 4
x2 = (7-1)/2 = 6/2 = 3
Ответ: 3,4,0

Answer 2

$x^3-7x^2+12x=0 \\ x(x^2-7x+12)=0 \\ x_1=0 \\ x^2-7x+12=0 \\ D=b^2-4ac=(-7)^2-4*1*12=49-48=1 \\ x_2= \frac{7- \sqrt{1} }{2}=3 \\ x_3= \frac{7+ \sqrt{1} }{2}=4$

Answer 3

Solution to the Equation: x^3 - 7x^2 + 12x = 0

To solve the equation x^3 - 7x^2 + 12x = 0, we need to find the values of x that satisfy the equation. Let's break down the solution step by step.

Step 1: Factor out x from the equation: x(x^2 - 7x + 12) = 0

Step 2: Solve for x by setting each factor equal to zero: x = 0 or x^2 - 7x + 12 = 0

Step 3: Solve the quadratic equation x^2 - 7x + 12 = 0: To solve the quadratic equation, we can either factor it or use the quadratic formula. Let's factor it: (x - 3)(x - 4) = 0

Step 4: Solve for x by setting each factor equal to zero: x - 3 = 0 or x - 4 = 0

Step 5: Solve for x in each equation: x = 3 or x = 4

Therefore, the solutions to the equation x^3 - 7x^2 + 12x = 0 are x = 0, x = 3, and x = 4.

Note: The solutions to the equation were obtained by factoring the equation and solving the resulting quadratic equation. The factors of the quadratic equation were found to be (x - 3) and (x - 4)