PriyankaPalit7 wrote:

Is x² - y > 1/y² where y is non-zero?

(1) x < y

(2) x² < y²

\(x^2\) - y > 1/\(y^2\)

\(x^2\) - y - 1/\(y^2\) > 0

Lets try 2 first

(2) x² < y² or y^2 > x^2,

9 > 4, y can be -3 or 3 and x can be -2 or 2

1/4 > 1/16, y can be 1/2 or -1/2 and x can be 1/4 or -1/4

4 +3 - 1/9 > 0, This answers a yes to the question

1/16 - 1/2 - 1/4 < 0, This answers a no to the question

from 1)

x < y or y>x, here y & x can be again a fraction, integer or a number

1/2 > 1/4 or 3 > 2

1/16 - 1/2 - 1/4 < 0, This answers a no to the question

4 -3 - 1/9 > 0, This answers a yes to the question

The same test cases can be used again to show that after combining the 2, we wont get an unique answer

E

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