Solve for x
-1= (1/x) +(1/(x^2))
multipy both sides by x^2
-x^2=x+1
now solve it.
0=x^2+x+1
which is not easily solved
Using the quadratic formula
x=(-1+- sqrt(1-4))/2 but notice the sqrt is a sqrt(-3), which is an imaginary number, so your roots are complex, not real.
multiply each term by x^2, which is the LCM
- x^2 = x + 1
x^2 + x + 1 = 0
use the quadratic equation to find the two complex roots.
To solve for x in the equation -1 = 1/x + 1/(x^2), we need to find a common denominator for the two fractions on the right side of the equation.
First, let's rewrite the equation with a common denominator of x^2:
-1 = (x + x^2)/x^2
Next, multiply both sides of the equation by x^2 to eliminate the denominator:
-1 * x^2 = x + x^2
Simplifying further, we have:
-x^2 = x + x^2
Combine like terms by moving x^2 to the left side:
0 = 2x^2 + x
Now, we have a quadratic equation. To solve for x, we can rearrange the equation:
2x^2 + x = 0
Factor out the common term x:
x(2x + 1) = 0
From here, we can use the zero product property, which states that if a product of two terms is equal to zero, then at least one of the terms must be zero.
Setting each factor equal to zero:
x = 0
2x + 1 = 0
Solving the second equation:
2x = -1
x = -1/2
Therefore, the two solutions for x are x = 0 and x = -1/2.