Question

X^4=(x-12)^2 решите уравнение подробно пожалуйста

Answer 1

 Х в 4 степени = Х в квадрате +144
Х в 4 степени -Х в квадрате = 144
Х в квадрате = 144
Х=корень из144
Х=12

Answer 2

Solving the Equation x^4 = (x-12)^2

To solve the equation x^4 = (x-12)^2, we can follow these steps:

Step 1: Expand the equation Step 2: Simplify the equation Step 3: Solve for x

Let's go through each step in detail.

Step 1: Expand the Equation

To expand the equation x^4 = (x-12)^2, we need to square the binomial (x-12)^2. This can be done by multiplying the binomial by itself.

Expanding (x-12)^2: (x-12)(x-12) = x^2 - 12x - 12x + 144 = x^2 - 24x + 144

Now, the equation becomes: x^4 = x^2 - 24x + 144

Step 2: Simplify the Equation

To simplify the equation x^4 = x^2 - 24x + 144, we need to move all the terms to one side of the equation to set it equal to zero.

Rearranging the equation: x^4 - x^2 + 24x - 144 = 0

Step 3: Solve for x

To solve the equation x^4 - x^2 + 24x - 144 = 0, we can use various methods such as factoring, completing the square, or using the quadratic formula. However, in this case, the equation is a quartic equation, which means it has a degree of 4.

Solving quartic equations can be complex and may require advanced techniques. In this case, it is recommended to use numerical methods or a graphing calculator to find the approximate solutions.

Unfortunately, without additional information or constraints, it is not possible to provide the exact solutions to the equation x^4 = (x-12)^2. However, you can use numerical methods or a graphing calculator to find the approximate solutions.

I hope this helps! Let me know if you have any further questions.