Determine all the values of y that satisfy the equation:y⁴-13y²+36=0

Answer 1

To determine all the values of y that satisfy the equation, we can use factoring or the quadratic formula.

Let's start by factoring the equation:

y⁴ - 13y² + 36 = 0

We can see that this is a quadratic equation in terms of y²:

(y² - 4) (y² - 9) = 0

Now, let's solve each factor separately:

y² - 4 = 0
(y - 2)(y + 2) = 0
y = 2 or y = -2

y² - 9 = 0
(y - 3)(y + 3) = 0
y = 3 or y = -3

Therefore, the values of y that satisfy the equation are y = 2, y = -2, y = 3, and y = -3.