Question

find two functions defined implicitly by this equation.\\(x^2 + 3x + y^2 - 2 = 0\\)\\(y = pmsqrt{?}x^2 + x + \\)

Explanation:

Step1: Isolate \( y^2 \)

We start with the given equation \( x^2 + 3x + y^2 - 2 = 0 \). To isolate \( y^2 \), we move the other terms to the right side of the equation. This gives us \( y^2=-x^2 - 3x + 2 \).

Step2: Solve for \( y \)

To solve for \( y \), we take the square root of both sides. Remember that when we take the square root of a quantity, we get both a positive and a negative root. So, \( y=\pm\sqrt{-x^2 - 3x + 2} \).

Answer:

The coefficient of \( x^2 \) is \(-1\), the coefficient of \( x \) is \(-3\), and the constant term is \( 2 \). So the functions are \( y = \pm\sqrt{-1x^2-3x + 2} \)