Bunuel wrote:

What is the value of x?

(1) 4/x + 4 + x = 0

(2) 6/x + 1 = x

St.1:: 4/x + 4 + x = 0

or x^2 + 4*x + 4 = 0

or (x+2)^2 = 0

so, we have two cases (x+2) = 0 and -(x+2) = 0. Since this is not inequality, we have x= -2 in both cases. hence Sufficient.

St.2 :: 6/x + 1 = x

or 6 + x = x^2

or x^2 -x -6 = 0

To express it in terms of factors i.e (a-b)^2 , the middle term must equal 2ab. a = x => 2*x*b = x => b = (1/2) or 0.5

So, we have (x^2 -x -6) = (x-0.5)^2 - (25/4)

or (x-0.5)^2 - (5/2)^2=0

this is of form a^2 - b^2 = (a+b)(a-b)

solving , we get (x+2)(x-3) = 0

x= -2 or 3 --------> two values. Not sufficient.

So, "A" is the answer in my opinion.

_________________

------------------------------

"Trust the timing of your life"

Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq