Question

X^2+1/x + x/ x^2=2,9

Answer 1

нужно умножить всё на х^2

общий знаменатель х^2

х^2+ x + x = 2.9 x^2

1.9x^2 + x = 0

x ( 1.9 x + 1 ) = 0

x = 0

или

1.9x + 1 = 0

x = - 19/10

Answer 2

To solve the equation $x^2 + \frac{1}{x} + \frac{x}{x^2} = 2.9$, we'll start by simplifying it:

First, let's combine the fractions on the left-hand side with a common denominator:

$\frac{x^3 + 1 + x^2}{x^2} = 2.9$

Next, multiply both sides by $x^2$ to eliminate the denominator:

$x^3 + 1 + x^2 = 2.9x^2$

Rearrange the terms:

$x^3 + 1 - 2.9x^2 + x^2 = 0$

Combine like terms:

$x^3 - 1.9x^2 + 1 = 0$

Now we have a cubic equation. To solve it, we can either use numerical methods or factor it if possible. Unfortunately, the given equation doesn't have any rational roots, so we'll resort to numerical methods.

Using a numerical solver, we find that one of the approximate solutions is $x \approx 0.6717$. The other two solutions are complex numbers.

Please note that the given equation may have more solutions, but we can only provide an approximation for one of them.