Bunuel wrote:

What is the value of \(xy?\)

(1) \(x^2y^2+2xy\pi-3\pi^2 = 0\)

(2) \(xy>-9.5\)

Kudos for a correct solution.

Took 9+ min to solve this, BUT happy could do it of my own. Sharing my analysis..

Find 'xy'

Statement 1 \(x^2y^2+2xy\pi-3\pi^2=0\)

=> Let xy=m , substituting in the above equ

=> \(m^2+2m\pi-3\pi^2=0\)

=>

or \(m^2+2m\pi-4\pi^2+\pi^2=0\)

=> \((m^2+2m\pi+\pi^2)-4\pi^2=0\)

=> \((m+\pi)^2-4\pi^2=0\)

=> \((m+\pi)^2-(2\pi)^2=0\)

=> \((m+\pi-2\pi)(m+\pi+2\pi)=0\) ----

from\((a^2-b^2)=(a-b)(a+b)\)

=> \((m-\pi)(m+3\pi)=0\)

=> \(m=\pi\)

or \(-3\pi\)

=> i.e \(xy=\pi\)

or \(-3\pi\)

=> Since 2 values of 'xy'. Therefore Stat 1 NOT SUFFICIENT

Statement 2 xy>-9.5

=> 'xy' can have any value > -9.5 i.e -9.4, -9.1 ...etc

=> Therefore NOT SUFFICIENT

BOTH Stat 1 & 2

=> 'xy'= 3.14 or -9.42 from Stat 1

=> xy>-9.5 from stat 2

=> AGAIN 'xy' has 2 values. Therefore NOT SUFFICIENT

Therefore 'E'

Thanks

Dinesh