x2 + 12/x2 = 7

(v) x² + ¹²/_x² = 7

Sol. x² + ¹²/_x² = 7

Multiplying by x² , we get

x⁴ + 12 = 7x²

∴ x⁴ – 7x² + 12 = 0

∴ (x²)²  - 7x² +12 = 0

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

Substituting x² = m we get,

m² – 7m + 12 = 0

∴  m² – 4m – 3m + 12 = 0

∴ m (m – 4) – 3 (m – 4) = 0

∴ (m – 4) (m – 3) = 0

∴  m – 4 = 0 or m – 3 = 0

∴  m = 4 or m = 3

Resubstituting m = x² we get,

x² = 4 or x² = 3

∴ x = ±√4 or x = ±√3

∴ x = ±2  or x = ±√3