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Question
Solve the quadratic equation : 3x4 - 13x2 +10 = 0.
Solution
3x4 - 13x2 +10 = 0
∴ 3(x2)2 - 13x2 + 10 = 0
[∵(am)n = am×n]
Substituting x2 = m we get,
3m2 - 13m + 10 = 0
∴ 3m2 - 3m - 10m + 10 = 0
∴3m (m - 1) - 10 (m -1)= 0
∴ (m – 1) (3m – 10) = 0
∴ m – 1 = 0 or 3m – 10 = 0
∴ m = 1 or 3m = 10
∴ m = 1 or m = `10/3`
Resubstituting m = x2 we get,
x2 = 1 or x2 = `10/3`
∴ x = ±√1 or x = ±`√(10/3)`
∴ x = ±1 or x = ±`√(10/3)`
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