Question

Решить бы уравнение x⌃4 +1-(x-2)⌃4=2x⌃2

Answer 1

эти стрелочки "умножение"?

Если да то -1

Answer 2

To solve the equation x^4 + 1 - (x - 2)^4 = 2x^2, we'll follow these steps:

Step 1: Expand (x - 2)^4 Step 2: Substitute the expansion into the original equation Step 3: Simplify the equation and set it to zero Step 4: Solve the resulting quadratic equation for x

Let's start:

Step 1: Expand (x - 2)^4

Using the binomial expansion formula, (a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4, where a = x and b = 2:

(x - 2)^4 = x^4 - 4x^3(2) + 6x^2(2)^2 - 4x(2)^3 + 2^4 (x - 2)^4 = x^4 - 8x^3 + 24x^2 - 32x + 16

Step 2: Substitute the expansion into the original equation

Now our equation becomes:

x^4 + 1 - (x^4 - 8x^3 + 24x^2 - 32x + 16) = 2x^2

Step 3: Simplify the equation and set it to zero

Let's combine like terms:

x^4 + 1 - x^4 + 8x^3 - 24x^2 + 32x - 16 = 2x^2

Simplifying further:

8x^3 - 24x^2 + 32x - 15 = 2x^2

Bringing all terms to one side of the equation:

8x^3 - 26x^2 + 32x - 15 = 0

Step 4: Solve the resulting quadratic equation for x

Unfortunately, this equation is not a quadratic equation, but a cubic equation due to the x^3 term. Solving cubic equations can be more complex and usually requires numerical methods or specialized techniques.

To get an approximate solution, you can use numerical methods like the Newton-Raphson method or graphing utilities to find the roots. Alternatively, if there is a specific value of x you are interested in, you can substitute it into the equation and calculate the result.

If you provide a specific value of x you want to evaluate or if you need further assistance, feel free to let me know!