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The solution set of the inequality is of form (a+b). x/((1-x) 1/2 +x 1/2 )-x/((1-x) 1/2 -x 1/2 )>2/x 1/2 The value of a+b= (a)14 (b)infinite (c)3/2 (d)11/4
x/((1-x)1/2 +x1/2 )-x/((1-x)1/2-x 1/2)>2/x1/2 x3/2[((1-x)1/2 -x1/2 ) - ((1-x)1/2 +x1/2 )]>2[((1-x) -x )] -2x2 > 2(1-2x) x2 -2x+1>0 (x-1)2>0 always true, thus infinite is the answer
x/((1-x)1/2 +x1/2 )-x/((1-x)1/2-x 1/2)>2/x1/2
x3/2[((1-x)1/2 -x1/2 ) - ((1-x)1/2 +x1/2 )]>2[((1-x) -x )]
-2x2 > 2(1-2x)
x2 -2x+1>0
(x-1)2>0
always true,
thus infinite is the answer
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