Question
If (x24Â +Â 1)/x12Â = 7, then
the value of (x72Â +Â 1)/x36Â isÂSolution
(x24 + 1)/x12 = 7 ⇒ x24/x12  + 1/x12  = 7 ⇒ x12 + 1/x12   = 7 ∴ (x72 + 1)/x36 = x72/x36 + 1/x36   = x36 + 1/x36   =  (x12 + 1/x12 )3 – 3 × x12 × 1/x12  (x12 + 1/x12)  ∵ (a + b)³ = a³ + b³ + 3ab (a + b) = 7³ - 3 × 7 = 343 – 21 = 322
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