Question

If x = 3 + 2√2, then find whether x-1/x is irrational or rational.

Answer 1

therefore it is irrational

Answer 2

$\frac{1}{x} = \frac{1}{3-2 \sqrt{2} } = \frac{1}{ \sqrt{9}- \sqrt{8}} = \frac{ \sqrt{9}- \sqrt{8}} { (\sqrt{9}- \sqrt{8})( \sqrt{9}+ \sqrt{8})} = \sqrt{9} - \sqrt{8} =3-[tex]x - \frac{1}{x} =3+ \sqrt{8} - (3- \sqrt{8} )=2 \sqrt{8}$ \sqrt{8} [/tex]

∴it is irrartional