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Question

7y4 – 25y2 + 12 = 0

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Solution

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 =47
On substituting m = y2, we get:
=> y2 = 3 or y2 =47
=> y = ±3 or y = ± 27
Thus, the solutions of the given equation are ±3 , ± 27.

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