Determine all the values of y that satisfy the equation:y⁴-13y²+36=0
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.
To determine all the values of y that satisfy the equation y⁴ - 13y² + 36 = 0, we can use factoring.
Let's rewrite the equation as a quadratic equation by substituting y² with x:
x² - 13x + 36 = 0
Now, let's factor this quadratic equation:
(x - 4)(x - 9) = 0
Setting each factor to zero, we have two possible values for x:
x - 4 = 0 --> x = 4
x - 9 = 0 --> x = 9
Since x = y², we can substitute back into the equation to find the values of y:
y² = 4 --> y = ±2
y² = 9 --> y = ±3
Therefore, the values of y that satisfy the equation y⁴ - 13y² + 36 = 0 are y = ±2 or y = ±3.