Question

(x+5)^4-10(x+5)^2+9=0 решение

Answer 1

Объяснение:

використання оберненої заміни

Answer 2

To solve the quadratic equation $(x+5)^4 - 10(x+5)^2 + 9 = 0$, you can use a substitution to simplify the equation. Let $y = (x+5)^2$. Then the equation becomes a quadratic equation in terms of $y$:

$y^2 - 10y + 9 = 0$

Now, you can factor this quadratic equation or use the quadratic formula to find the values of $y$. Factoring, you get:

$(y - 1)(y - 9) = 0$

So, $y = 1$ or $y = 9$.

Now, substitute back $y = (x+5)^2$:

1. $x+5)^2 = 1$
2. $x+5 = \pm 1$

Solving these equations will give you the values of $x$.

For the first equation:

$x + 5 = 1 \quad \text{or} \quad x + 5 = -1$

Solving for $x$ in each case:

1. $x = 1 - 5 = -4$
2. $x = -1 - 5 = -6$

For the second equation:

$x + 5 = 9 \quad \text{or} \quad x + 5 = -9$

Solving for $x$ in each case:

1. $x = 9 - 5 = 4$
2. $x = -9 - 5 = -14$

So, the solutions to the original equation are $x = -4, -6, 4, -14$.