Question

7y⁴ – 25y² + 12 = 0

Answer 1

Given: 7y⁴ – 25y² + 12 = 0
Let y² = m
Then, the equation can be written as:
7m² – 25m + 12 = 0
On splitting the middle term –25m as –21m – 4m, we get:
7m² – 21m – 4m + 12 = 0
=> 7m(m – 3) –4(m – 3) = 0
=> (m – 3)(7m – 4) = 0
=> m – 3 = 0 or 7m – 4 = 0
=> m = 3 or m =$\frac{4}{7}$
On substituting m = y², we get:
=> y² = 3 or y² =$\frac{4}{7}$
=> y = ±$\sqrt{3}$ or y = ± $\frac{2}{\sqrt{7}}$
Thus, the solutions of the given equation are ±$\sqrt{3}$ , ± $\frac{2}{\sqrt{7}}$.