Complex Numbers And Quadratic Equations question 717
Question: If $ x=2+{2^{2/3}}+{2^{1/3}}, $ then $ x^{3}-6x^{2}+6x= $ [MNR 1985]
Options:
A) 3
B) 2
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ x=2+{2^{2/3}}+{2^{1/3}}\Rightarrow x-2={2^{2/3}}+{2^{1/3}} $ Cubing both sides, we get $ x^{3}-8-6x^{2}+12x=6+6(x-2) $
Þ $ x^{3}-6x^{2}+6x=2 $ .
BETA
