3x4 – 13x2 + 10 = 0

(vii) 3x⁴ – 13x² + 10 = 0 

Sol. 3x⁴ – 13x² + 10 = 0

∴  3 (x²)² – 13x² + 10 = 0 

                                    [ ∵ (a^m)ⁿ = a^{m× 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)