Answers

2014-10-17T13:29:32+05:30
X²+x+1 = 0
⇒  x²+1 = -x
⇒  (x²+1)/x = -1
Now,
    [ x^{3}+ \frac{1}{ x^{3} }]  ^{3} = [ (x+ \frac{1}{x} )^{3}-3.(x).(1/x)(x+1/x)  ]^{3}  \\  \\ or,  (x+ \frac{1}{x} )^{3} [( x+ \frac{1}{x}) ^{2} -3]^{3}

or,   (\frac{ x^{2} +1}{x}) ^{3} [( \frac{ x^{2} +1}{x} )^{2}-3] ^{3}

Put the value of (x²+1)/x from Equn (1) ,

  =(-1)³  [(-1)²-3]³

=  -(-2)³ = 8
1 1 1
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thank u very much karthik. I have posted one more question please help me out with that too.
thanks