If 4x2y 128 and 33x 32y ndash 9xy 0 then the value of x y can be equal to ........

Quantitative Aptitude (CDS) Number System

If 4^x2^y = 128 and 3^3x 3^2y – 9xy = 0, then the value of x + y can be equal to?

4^x. 2^y = 128 and

3^3x . 3^2y − 9^xy = 0

2^2x . 2^y = 128 = (2)⁷. 3^3x+2y [ $\because$ 9 = 3²]

=> 2x + y = 7 => 3x + 2y = 2xy… . (1)

=> y = 7 − 2x … . (2)

Substitute this value of y in (2) we get

3x + 2(7 − 2x) = 2x(7 − 2x)

4x²− 15x + 14 = 0

(4x − 7)(x − 2) = 0

Either 4x − 7 = 0 or x − 2 = 0

$=> x=\frac{7}{4} \, or\, x = 2 \; \; \; => x \neq \frac{7}{4}\; =>x=2\: \: \: =>x+y=2 + 3=5$

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