Question

solve the equation using the method of your choice.\\(y^{2}-4y + 8 = 0\\)\\(\\)\\(\\)the solution set is \\(\\{\square\\}\\).\\(\\)\\(\\) (type an exact answer, using radicals as needed. express complex numbers in terms of \\(i\\). use a comm

Explanation:

Step1: Identify quadratic coefficients

For $y^2 - 4y + 8 = 0$, we have $a=1$, $b=-4$, $c=8$.

Step2: Apply quadratic formula

Quadratic formula: $y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$y = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(8)}}{2(1)}$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{16 - 32} = \sqrt{-16} = 4i$

Step4: Simplify the expression

Substitute discriminant back:
$y = \frac{4 \pm 4i}{2} = 2 \pm 2i$

Answer:

$\{2+2i, 2-2i\}$