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by sanju09 » Mon Mar 12, 2012 2:31 am
If y^3 - x y^2 - 14 x^2 y + 24 x^3 = 0, then which of the following is NOT true for y?
I. y = 2 x
II. y = 3 x
III. y = 4 x
(A) III only
(B) II only
(C) I only
(D) III & II
(E) III & I
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by killer1387 » Mon Mar 12, 2012 2:44 am
IMO A
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by Anurag@Gurome » Mon Mar 12, 2012 5:50 am
sanju09 wrote:If y^3 - x y^2 - 14 x^2 y + 24 x^3 = 0, then which of the following is NOT true for y?
I. y = 2 x
II. y = 3 x
III. y = 4 x
(A) III only
(B) II only
(C) I only
(D) III & II
(E) III & I
(I) y = 2x
(2x)^3 - x (2x)^2 - 14 x^2 (2x) + 24 x^3 = 0
8x^3 - 4x^3 - 28x^3 + 24x^3 = 0
0 = 0 holds true.

(II) y = 3x
(3x)^3 - x (3x)^2 - 14 x^2 (3x) + 24 x^3 = 0
27x^3 - 9x^3 - 42x^3 + 24x^3 = 0
0 = 0 holds true.

(III) y = 4x
(4x)^3 - x (4x)^2 - 14 x^2 (4x) + 24 x^3 = 0
64x^3 - 16x^3 - 56x^3 + 24x^3 = 0
16x^3 = 0 does NOT hold true.

The correct answer is A.
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