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Quantitative Aptitude

Solving Inequalities

I. 9 x 2-9 x ...

Question

I. $9 x^{2} - 9 x + 2 = 0$
II. $9 y^{2} - 3 y - 2 = 0$

A

if x > y

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B

if x < y

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C

if x <= y

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D

if x = y or relationship between x and y cannot be determined

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Solution

The correct option is D if x = y or relationship between x and y cannot be determined
$9 x^{2} - 9 x + 2 = 0 9 x^{2} - 6 x - 3 x + 2 = 0 3 x (3 x - 2) - 1 (3 x - 2) = 0 (3 x - 2) (3 x - 1) = 0 x = \frac{2}{3}, \frac{1}{3}$
$A l s o, 9 y^{2} - 3 y - 2 = 0 9 y^{2} - 6 y + 3 y - 2 = 0 3 y (3 y - 2) + 1 (3 y - 2) = 0 (3 y - 2) (3 y + 1) = 0 y = - \frac{1}{3}, \frac{2}{3}$
$∴$ Relationship between x and y cannot be determined.

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