Question

X^2+x+(4/x^2)=(2/x)+4

Answer 1

Ответ: 4 корня: -2, -корень 2, 1 , корень 2

Answer 2

To solve the equation $x^2 + x + \frac{4}{x^2} = \frac{2}{x} + 4$, we can follow these steps:

Step 1: Get rid of the fractions by multiplying every term by $x^2$ to eliminate the denominators: $x^2 \cdot \left( x^2 + x + \frac{4}{x^2} \right) = x^2 \cdot \left( \frac{2}{x} + 4 \right)$.

Step 2: Simplify the equation: $x^4 + x^3 + 4 = 2x + 4x^2$.

Step 3: Move all the terms to one side of the equation to set it to zero: $x^4 + x^3 + 4 - 2x - 4x^2 = 0$.

Step 4: Rearrange the terms in descending order of $x$: $x^4 + x^3 - 4x^2 - 2x + 4 = 0$.

Unfortunately, this equation does not have a straightforward algebraic solution. You can solve it numerically using methods like Newton-Raphson or using software like graphing calculators or computational tools. If you're looking for an approximate solution, you can use numerical methods to find the roots.