Answer:
The roots are {-3, -2, 2, 3}.
Step-by-step explanation:
The trick here is to represent y² by some other letter, such as x. If we do that, then y^4-13y^2+36=0 becomes x² - 13x + 36 = 0.
Recognize that the factors -4 and -9 of 36 sum up to 13. Thus,
x² - 13x + 36 = 0 is equivalent to (x - 4)(x - 9) = 0, and x = 4 or x = 9.
Recall that x = y².
When x = 4: y² = 4, and so y = ±2.
When x = 9, y² = 9, and so y = ±3.
The roots are {-3, -2, 2, 3}.
