Question

X²(2 - x)² = 1+ 2(1 – x)²​

Answer 1

Ответ:

x$_{1}$=-1, x$_{2}$=1, x$_{3}$=3

Объяснение:

(x(2-x)$)^{2}$=1+2(1-2x+$x^{2}$)

(2x-$x^{2}$$)^{2}$=1+2-4x+2

2$x^{2}$-4$x^{3}$+$x^{4}$-3+4x=0

(x-1)($x^{3}$-3$x^{2}$-x+3)=0

x-1=0

x-3=0

$x^{2}$-1=0

x=1

x=3

x=-1

x=1

x$_{1}$=-1, x$_{2}$=1, x$_{3}$=3

буду благодарна, если отметите мой ответ как "лучший" с помощью короны

Answer 2

To solve the equation $x^2(2 - x)^2 = 1 + 2(1 - x)^2$, follow these steps:

Step 1: Expand both sides of the equation: Expand the terms on both sides of the equation to simplify it. On the left side: $x^2(2 - x)^2 = x^2(4 - 4x + x^2) = 4x^2 - 4x^3 + x^4$ On the right side: $1 + 2(1 - x)^2 = 1 + 2(1 - 2x + x^2) = 1 + 2 - 4x + 2x^2$

Step 2: Rewrite the equation: Now we have the equation as: $4x^2 - 4x^3 + x^4 = 3 + 2x^2 - 4x$

Step 3: Bring all terms to one side of the equation: Rearrange the equation: $x^4 - 2x^2 - 4x^3 + 4x - 3 = 0$

Step 4: Factor the equation: This equation doesn't seem to have any simple factoring. You might need to use numerical or graphical methods to approximate the solutions.

Step 5: Solve numerically or graphically: Since the equation is a quartic equation and might not have simple exact solutions, you might need to use numerical methods like the Newton-Raphson method or graphical methods to find approximate solutions.

If you have access to a graphing calculator or software, you can graph the functions $y = x^4 - 2x^2 - 4x^3 + 4x - 3$ and $y = 0$ and find the x-values where they intersect, which will be the solutions to the equation.

Alternatively, you can use numerical methods like the Newton-Raphson method or bisection method to find approximate solutions. These methods might require some programming or the use of mathematical software.

Keep in mind that quartic equations can be quite complex to solve, and in many cases, exact solutions might not be possible, so numerical methods are often used to find approximate solutions.