35y2 + 12/y2 = 44

(iv) 35y² + ¹²/_y² = 44

Sol. 35y² + ¹²/_y² = 44

Multiplying throughout by y² we get,

35y⁴ + 12 = 44y²

∴  35 (y²)² – 44y² + 12 = 0

 [ ∵ (a^m)ⁿ = a^{m× n}]

Substituting y² = m we get,

35m² – 44m + 12 = 0

∴ 35m² – 14m – 30m + 12 = 0

 ∴ 7m (5m – 2) – 6 (5m – 2) = 0

 ∴ (5m – 2) (7m – 6) = 0

 ∴ 5m – 2 = 0 or 7m – 6 = 0

 ∴ 5m = 2 or 7m = 6

∴ m = ²/₅  or m = ⁶/₇

Resubstituting,  m = y², we get;

∴ y² =  ²/₅  or y² = ⁶/₇

∴  y = ±√(²/₅)    or y = ±√(⁶/₇)