If x2n +1/x2n =k Let xn -1/xn =y (xn +1/xn)2 = x2n +1/x2n +2 (xn +1/xn)2 =k+2 Let xn +1/xn =z z2 = k+2 … (1) Using the identity for the square of a difference: y² = z2-4 Since z2 =k+2: y² = (k+2)-4 y² = k -2 Therefore- y = √ k-2 xn -1/xn =√ (k-2)
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