Elementary Functions

[Aman verma]

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

[thephoenix]

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

[mj78ind]

@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.......

[STEVEN SPIELBERG]

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

[Aman verma]

OAE. Thanks to all !