Answer:
y = ±√3 and ±2i
Explanation:
Given the equation y⁴+y²-12 = 0
(y²)²+y²-12 = 0
Let P = y²
Substitute
P²+P-12 = 0
Factorize:
P²+4P-3P -12 = 0
P(P+4)-3(P+4) = 0
(P-3)(P+4) = 0
P-3 = 0 and P+4 = 0
P = 3 and -4
When P = 3
y² = 3
y = ±√3
When P = -4
y² = -4
y² = ±√-4
y = ±2i
Hence the value of y is ±√3 and ±2i