If 9x 3y 2187 and 23x22y minus 4xy 0 then what can be the value of x y ........

Quantitative Aptitude (CDS) Simplification

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If 9^x 3^y = 2187 and 2^3x2^2y − 4^xy = 0 , then what can be the value of (x + y) ?

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Explanation:

$9^{x}\times3^{y}=2187$
=> 3^2xx3^y=2187
=> 3^2x^+2y=2187=3⁷
=>2x+y=7.................(i)
Also 2^3x+2y =2^2xy
therefore 3x + 2y = 2xy.............(ii)
from (i) and (ii) , we get
3x+2(7 - 2x) = 7
Solving we get
4x² - 15x + 14 = 0
(x - 2)((4x - 7)=0
x = 2 or x = 7/4
if x = 2
y = 7 - 2x = 7 - 4 = 3
x + y = 5