How many real solutions are there to the equation x^2 =1/(x+3)
There are no real solutions to the equation x^2 = 1/(x+3).
To see this, we can try to solve for x by isolating x on one side of the equation. Multiplying both sides of the equation by x+3, we get x^2(x+3) = 1. Expanding the left-hand side, we get x^3 + 3x^2 = 1.
This equation is a polynomial equation of degree 3. Polynomial equations of degree 3 have at most 3 roots, which can be real or complex numbers. In this case, the roots of the equation x^3 + 3x^2 - 1 = 0 are complex numbers. Therefore, there are no real solutions to the equation x^2 = 1/(x+3).