Question

If x = 3 + 2 √2, find the value of (x½-1/x½​

Answer 1

Answer:

this should help you

Step-by-step explanation:

$( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} = x + \frac{1}{x} + 2( \sqrt{x} )( \frac{1}{ \sqrt{x} } ) \\ ( \sqrt{x } + \frac{1}{ \sqrt{x} } ) {}^{2} = 3 + 2 \sqrt{2} + \frac{1}{3 + 2 \sqrt{2} } + 2 \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} }) {}^{2} = \frac{(3 + 2 \sqrt{2}) {}^{2} + 1 + 2(3 + 2 \sqrt{2}) }{3 + 2 \sqrt{2} } \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} = \frac{9 + 8 + 12 \sqrt{2} + 1 + 6 + 4 \sqrt{2} }{3 + 2 \sqrt{2} } \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} }) {}^{2} = \frac{24 + 16 \sqrt{2} }{3 + 2 \sqrt{2} } \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} } ) {}^{2} = 8 \\ ( \sqrt{x} + \frac{1}{ \sqrt{x} }) {}^{2} = 2 \sqrt{2}$