Question

Уравнение х(х+4)^2=12(х+4) Ответ: -6 ; -4 ; 2 Как получили х= -4

Answer 1

Х(х+4)^2=12(х+4)
х(х+4)-12(х+4)=0
(х+4)*(х(х+4)-12)=0
(х+4)*(х^2+4х-12)=0
приравнимаем первую и вторую часть к 0 и решаем относительно х
в первом случае будет х+4=0; х=-4

Answer 2

X(x+4)²=12(x+4)
x(x+4)²-12(x+4)=0
(x+4)(x(x+4)-12)=0
(x+4)(x²+4x-12)=0
a)x+4=0, x=-4
b)x²+4x-12=0,D=16+48=64,√D=√64=8
   x=(-4+8)/2=2 , x=(-4-8)/2=-6
x=-4 , x=2, x=-6
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Answer 3

To solve the equation $x(x+4)^2 = 12(x+4)$ and find the solution $x = -4$, we'll follow these steps:

Step 1: Set the equation equal to zero. $x(x+4)^2 - 12(x+4) = 0$

Step 2: Factor out the common term $(x+4)$ from both terms on the left-hand side. $x(x+4)[(x+4) - 12] = 0$

Step 3: Simplify the expression inside the square brackets. $x(x+4)(x - 8) = 0$

Step 4: Now, we have a product of three terms equal to zero. The equation will be true if any of the individual terms is equal to zero. So, we have three possible cases:

a) $x = 0$ b) $x + 4 = 0 \Rightarrow x = -4$ c) $x - 8 = 0 \Rightarrow x = 8$

However, the answer provided states $x = -6, -4, 2$, not $x = -4$. So, let's check if $x = -6$ and $x = 2$ satisfy the original equation:

For $x = -6$: $x(x+4)^2 = (-6)(-6+4)^2 = (-6)(-2)^2 = (-6)(4) = -24$ $12(x+4) = 12(-6+4) = 12(-2) = -24$

The left-hand side and right-hand side of the equation are equal for $x = -6$.

For $x = 2$: $x(x+4)^2 = (2)(2+4)^2 = (2)(6)^2 = (2)(36) = 72$ $12(x+4) = 12(2+4) = 12(6) = 72$

The left-hand side and right-hand side of the equation are equal for $x = 2$.

Therefore, the correct solution to the equation is $x = -6, -4, \text{ and } 2$, not just $x = -4$.