CAT 2023 Slot 1 Solved Paper

© examsiri.com

Question : 48 of 66

Marks: +1, -0

If

x

and

y

are real numbers such that

x^2+(x-2 y-1)^2=-4 y(x+y)

, then the value

x-2 y

is

$0$
$1$
$-1$
$2$

Solution:

Given,

x^2+(x-2 y-1)^2=-4 y(x+y)

⇒

\;x^2+4 x y+4 y^2+(x-2 y-1)^2=0

⇒

(x+2 y)^2+(x-2 y-1)^2=0

For the L.H.S. of the equation to be 0 , each of the square terms should be 0 (as squares cannot be negative)

⇒ x-2 y-1=0 ⇒ x-2 y=1

© examsiri.com

Go to Question:

Prev Question

Next Question