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Elementary Functions

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by Aman verma » Tue May 18, 2010 1:31 am
Q: If f(x) = 64x^3 + 1/( x)^3 and a , b are the roots of 4x + 1/x = 2 , then

(I) f(a) = - 24
(II) f(a) = - 16
(III)f(b) = - 16

(a) Only I

(b) Only II

(c) Both I and III

(d) Both I and II

(e) Both II and IIII
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by thephoenix » Tue May 18, 2010 2:25 am
Aman verma wrote:Q: If f(x) = 64x^3 + 1/( x)^3 and a , b are the roots of 4x + 1/x = 2 , then

(I) f(a) = - 24
(II) f(a) = - 16
(III)f(b) = - 16

(a) Only I

(b) Only II

(c) Both I and III

(d) Both I and II

(e) Both II and IIII
IMO E
from the information given in question f(x)=-16 ---->f(a)=-16 and f(b)=-16
f(x)=64x^3+1/x^3=[(4x+1/x)^3-3(4x)(1/x)(4x+1/x)]; since 4x+1/x=2 we get f(x)=2^3-3*4*2=8-24=-16
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by mj78ind » Tue May 18, 2010 3:43 am
@Aman

There are no real roots for the equation - 4x + 1/x = 2, since it transforms into 4x^2 - 2x + 1 = 0, where b^2-4ac for the quadritic is less than zero hence teh roots will be imaginary.......
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by STEVEN SPIELBERG » Tue May 18, 2010 8:39 am
Aman verma wrote:Q: If f(x) = 64x^3 + 1/( x)^3 and a , b are the roots of 4x + 1/x = 2 , then

(I) f(a) = - 24
(II) f(a) = - 16
(III)f(b) = - 16

(a) Only I

(b) Only II

(c) Both I and III

(d) Both I and II

(e) Both II and IIII
What's the OA
I want to win an OSCAR on the GMAT !!!
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by Aman verma » Tue May 18, 2010 10:58 pm
OAE. Thanks to all !
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