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Let f be a continuous and differentiable...

Let f be a continuous and differentiable function in `(x_(1),x_(2))`. If `f(x).f'(x)ge x sqrt(1-(f(x))^(4))` and `lim_(xrarrx_(1))(f(x))^(2)=1 and lim_(xrarrx) )(f(x))^(2)=(1)/(2)`, then minimum value of `(x_(1)^(2)-x_(2)^(2))` is

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