Question

(x^2+2x)^2-(x-1)^2=55

Answer 1

X^4+6x+2x^2-x^2-2x+1=55
x^4+x^2+4x+1=55
x^4+x^2+4x=54
Дальше не знаю как

Answer 2

Дальше обратная под становища пусть x2=t тогда x2+5x-54=0

Answer 3

Let's solve the equation step by step:

1. Expand the expressions on both sides of the equation:

   (x^2 + 2x)^2 - (x - 1)^2 = 55

   Expanding the squares: (x^4 + 4x^3 + 4x^2) - (x^2 - 2x + 1) = 55

2. Combine like terms:

   x^4 + 4x^3 + 4x^2 - (x^2 - 2x + 1) = 55

3. Distribute the negative sign on the right side:

   x^4 + 4x^3 + 4x^2 - x^2 + 2x - 1 = 55

4. Combine like terms:

   x^4 + 4x^3 + 3x^2 + 2x - 1 - 55 = 0

5. Simplify the equation:

   x^4 + 4x^3 + 3x^2 + 2x - 56 = 0

Now, we have a quartic equation (an equation of degree 4) in terms of x. Solving quartic equations can be quite involved, and there isn't a simple general formula for solving all quartic equations. You may need to use numerical methods or specialized software to find the solutions.

If you're looking for approximate solutions, you can use numerical methods like the Newton-Raphson method or graphing calculators/computer software to find the roots of this equation.