If a = (√2 - 1)1/3, then the value of (a-1/a)3 +3(a-1/a) is:
a = (√2 - 1)1/3 both sides cube a3= (√2 - 1) … (1) Now- (a-1/a)3 + 3(a-1/a) using formula (a-b)3 =a3-b3-3ab(a-b) =a3-1/a3 -3×a×1/a(a-1/a) +3(a-1/a) = a3-1/a3 -3(a-1/a) + 3(a-1/a) = a3-1/a3 Now put the value of a3. = (√2 - 1) -1/ (√2 - 1) = (√2 - 1) – [(√2 + 1)/ (√2 - 1) (√2 + 1)] = (√2 - 1- √2 - 1) =-1-1 =-2.
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