2y2 + 15/y2 = 12

(viii) 2y² + ¹⁵/_y² = 12

Sol.  2y² + ¹⁵/_y² = 12

Multiplying by y² , we get

2y⁴ + 15 = 12y²

∴ 2 (y²)² – 12y² + 15 = 0

[ ∵ (a^m)ⁿ = a^{m× n}]

Substituting y² = m we get,

2m² – 12m + 15 = 0

Comparing with am² + bm + c = 0 we a = 2, b = – 12, c = 15

b² – 4ac = (– 12)² – 4 (2) (15)

= 144 – 120

= 24

By Formula method,

m	=	-  b ± √(b2 – 4ac)
		2a
∴ m	=	-(- 12)± √24
		2(2)
∴ m	=	12 ± 2√6
		2
∴ m	=	2(6±√6)
		2
∴ xm	=	6±√6
		2
∴ m	=	6+√6	or	6 - √6
		2		2

Resubstituting m = y² we get,

y² = ^6+√6/₂   or  y²  =  ^{6 - √6} /₂   

∴ y = ±√(^6+√6/₂)    or   y = ±√(^{6 - √6} /₂)