Competitive Exams : Practice Set

Q. If x + 1/x = 3 then find x3+ 1/x3


Options: A) 18  B) 24  C) 27  D) 30


Solution


Use the identity:


(x+1/x)3 = x3+1/x3+3(x+1/x)


Given:


x + 1/x = 3


So,


33 = x3 + 1​/ x3 + 3(3)


27 = x3 + 1​/ x3  ​+ 9


Therefore,


x3+1/x3 = 27 – 9 = 18


Ans: A) 18


Shortcut


If  x + 1/x = 3


then


x3+1/x3 = a3−3a


Here: 33−3(3) = 27 − 9 = 18


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