KVPY SA Exam 05-Nov-2017 Question Paper

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Question : 8 of 80

Marks: +1, -0

If

72^x. 48^y = 6^{xy}

, where x and y are nonzero rational numbers, then x + y equals

3
$10/ 3$
–3
$-10 /3$

Solution:

72^{x} ⋅ 48^{y}=6^{x y}

⇒(2^{3} ⋅ 3^{2})^{x} ⋅(2^{4} ⋅ 3)^{y}=2^{x y} ⋅ 3^{x y}

Equating powers of 2 and 3 , we get

⇒ 3 x+4 y=x y . . .

eqn (1)

⇒ 2 x+3 y=x y . . .

eqn (2)
Subtract eqn(1) from eqn(2), we get

x=-3 y

Put this value of

x

in eqn (2)

-6 y+y=-3 y^{2}

⇒ y=\;{5}/{3}

and x=-5

x+y=-5+\;{5}/{3}=\;{-10}/{3}

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