CAT 2023 Set-1 | Quantitative Aptitude | Question: 1

Question

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

• A. $1$
• B. $2$
• C. $-1$
• D. $0$

   

Answer 1

First of all simlify the given  equation  and create it a  polynomial in X  which is

x^2 + +(-6*y - 2) x + 2y +1

now  find D in  term of y  

where we get  y = 0 ,y = + 2/3iota ,-2/3 iota  which is eliminated and  ony y  = 0;

if we put y = 0 in orginal equation  it will become ( x-1)^2  for which x = 1 is root  

the put  in desired equation which is 1

Answer 2

(D). 0 is the write answer