Question

X^4-26x^2+25=0 (x+3)^2-13(x+3)+36=0​

Answer 1

Ответ:1)x= -5

x= 5

X=1

X=-1

2)

x=1 x=6

Объяснение:

Answer 2

To solve the equations $x^4 - 26x^2 + 25 = 0$ and $(x+3)^2 - 13(x+3) + 36 = 0$, you can use a substitution method to simplify the equations.

Let's start with the first equation:

$x^4 - 26x^2 + 25 = 0$

This is a quadratic equation in terms of $x^2$. You can make a substitution to simplify it. Let $y = x^2$, then the equation becomes:

$y^2 - 26y + 25 = 0$

Now, you can solve this quadratic equation for $y$. Factoring is one way to do it:

$(y - 1)(y - 25) = 0$

Now, set each factor equal to zero and solve for $y$:

1. $y - 1 = 0$ → $y = 1$
2. $y - 25 = 0$ → $y = 25$

Now that you have the values of $y$, you can find the corresponding values of $x$ by taking the square root:

For $y = 1$: $x^2 = 1$ This gives two solutions: $x = 1$ and $x = -1$.

For $y = 25$: $x^2 = 25$ This also gives two solutions: $x = 5$ and $x = -5$.

So, for the first equation, you have four solutions: $x = 1$, $x = -1$, $x = 5$, and $x = -5$.

Now, let's move on to the second equation:

$(x+3)^2 - 13(x+3) + 36 = 0$

You can simplify this equation by making a substitution as well. Let $z = x + 3$, then the equation becomes:

$z^2 - 13z + 36 = 0$

Now, you can solve this quadratic equation for $z$. Factoring it:

$(z - 9)(z - 4) = 0$

Set each factor equal to zero and solve for (z:

1. $z - 9 = 0$ → $z = 9$
2. $z - 4 = 0$ → $z = 4$

Now that you have the values of $z$, you can find the corresponding values of $x$:

For $z = 9$: $x + 3 = 9$ This gives $x = 6$.

For $z = 4$: $x + 3 = 4$ This gives $x = 1$.

So, for the second equation, you have two solutions: $x = 6$ and $x = 1$.

In summary, the solutions to the equations are:

For $x^4 - 26x^2 + 25 = 0$: $x = 1$, $x = -1$, $x = 5$, and $x = -5$.

For $(x+3)^2 - 13(x+3) + 36 = 0$: $x = 6$ and $x = 1$.