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
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