For all numbers c and d, the operation @ is defined by c@d = c^2 - cd.
For all numbers c and d, the operation @ is defined by c@d = c^2 - cd. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
Answer/Solution
I and II
Steps/Work
c@d = c^2 - cd=c(c-d).... so c@d will be zero if c=d or c=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B
now lets look at the choices..
when x=y, it will be 0... so ok...
when we put xy=y, it is possible when x=1 and y any integer... so ok again
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible
only l and ll possible
answer: B