Question

(Х-2)*(Х*Х+8Х+16)=7(Х+4)

Answer 1

Если начать упрощение, то получится уравнение третьей степени. Пробуем разложить на множители левую часть уравнения.
(х-2)(х²+8х+16) - 7(х+4)=0
(х-2)(х+4)²-7(х+4)=0
(х+4)((х+2)(х+4)-7)=0
х+4 =0  или (х-2)(х+4)-7=0
х=-4                х²+2х-15=0
                               х=-5,х=3
Ответ: -4;-5;3.

Answer 2

To solve the equation (x - 2)(x^2 + 8x + 16) = 7(x + 4), we'll start by simplifying both sides of the equation and then solving for x.

Expanding the terms on the left side:

(x - 2)(x^2 + 8x + 16) = 7(x + 4) x(x^2 + 8x + 16) - 2(x^2 + 8x + 16) = 7x + 28

Now let's simplify further:

x^3 + 8x^2 + 16x - 2x^2 - 16x - 32 = 7x + 28 x^3 + 6x^2 - 7x - 32 = 7x + 28

Combining like terms:

x^3 + 6x^2 - 7x - 7x - 32 - 28 = 0 x^3 + 6x^2 - 14x - 60 = 0

Now we need to solve this cubic equation. Unfortunately, cubic equations don't have a general formula like quadratics do. We can either try to factor the equation or use numerical methods to approximate the roots.

By observing the equation, we can see that x = 2 is a root (since (x - 2) appears as a factor in the original equation). We can use long division or synthetic division to divide the equation by (x - 2):

Dividing x^3 + 6x^2 - 14x - 60 by (x - 2):

markdownCopy code
     x^2 + 8x + 30
 ___________________

x - 2 | x^3 + 6x^2 - 14x - 60 - (x^3 - 2x^2) _______________ 8x^2 - 14x - (8x^2 - 16x) _______________ 2x - 60 - (2x - 4) ___________ -56

The quotient is x^2 + 8x + 30, and the remainder is -56.

So, we have:

(x^3 + 6x^2 - 14x - 60) / (x - 2) = x^2 + 8x + 30 - (56 / (x - 2))

Now, the equation becomes:

x^2 + 8x + 30 - (56 / (x - 2)) = 0

To solve this equation, we can either use numerical methods or approximate the solutions graphically. Unfortunately, I can't provide the exact solutions without numerical methods.