Question

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Answer 1

Hope it helps you......

Answer 2

given,

$6x - {x}^{2} = 1 \\ = > {x}^{2} + 1 = 6x \\ = > x + \frac{1}{x} = 6$
------ (i)

now squaring, the given term and putting the value from eqn (i)...
${( \sqrt{x} - \frac{1}{ \sqrt{x} } ) }^{2} = x + \frac{1}{x} - 2 = 6 - 2 = 4 \\ ( \sqrt{x} - \frac{1}{ \sqrt{x} } ) = \sqrt{4} = 2$
so, answer = 2 ...