Solve the given equation: a4 – 3a2 + 2 = 0
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Answer:
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a4 – 3a2
+ 2 = 0
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Put a2 = m, then
the given equation will become
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∴ m2
– 3 m + 2 = 0
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∴ m2
– 2m – 1m + 2 = 0
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∴ m(m
– 2) – 1(m – 2) = 0
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∴ (m
– 2) (m – 1) = 0
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∴ m –
2 = 0 OR m – 1 = 0
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∴ m
= 2 OR m
= 1
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Now, re substituting m = a2
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∴ m = 2
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∴ m
= 1
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∴ a2
= 2
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∴ a2
= 1
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∴ a
= ± √2
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∴ a
= ± √1
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∴ a
= ± 1
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Solution Set: {√2, - √2, 1, -1 }
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