What is the value of x?

Question

What is the value of x?
 
(1) x^2 – y^2 = 0

(2) x/y + y/x = 0

niks18 · Answer

Statement 1:  (x-y)(x+y)=0 , so either  x-y=0  or  x+y=0 , in either case we have two variables and one equation. hence  insufficient

Statement 2: Solve it to get  \frac{(x^2+y^2)}{xy}=0

or  x^2+y^2 = 0 . Sum of two positive numbers is 0 only when both the numbers are 0

Hence  x=0 .  Sufficient

Option  B

pushpitkc · Answer

(1) x^2 – y^2 = 0
x^2 = y^2 , but this is not enough to answer 
the question to what is the value of x(Insufficient)

(2) x/y + y/x = 0
This equation can be re-written as x^2 + y^2=0
This is only when possible when x=y=0 (Sufficient)(Option B)

elainetianfong · Answer

In order to make (2) works, both x, y have to be different from 0. 
So, how can x = y = 0 ?
I don't think this is a valid solution.
Plz show the source of the question, thanks!

niks18 · Answer

Hi  elainetianfong

For the source of the question, kindly consult owner of the question  Bunuel

As far as the equation in statement 2 is concerned, in an equality if RHS is  0 , then LHS has to be  0 . Here the LHS is an algebraic expression that is not presented in its simplest form. We need to find the roots of this quadratic equation. Hence on simplification it yields  x^2+y^2  which will yield  x=y=0 . In graphical terms it will be a DOT in the x-y plane at the origin.

Hi  Bunuel  - can you provide more technical clarity on this.

What is the value of x?

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