Question

If x=3+2√2,check whether x+1/(x ) is a rational or irrational.solve with explanation...​

Answer 1

Answer:

☯️If x=3+2√2,check whether x+1/(x ) is a rational or irrational.solve with explanation...

$given \: x = 3 + 2 \sqrt{2}$

$= \frac{x + 1}{x}$

$= \frac{ 3 + 2 \sqrt{2} + 1}{ 3 + 2 \sqrt{2}}$

$= \frac{4 + 2 \sqrt{2} }{3 + 2 \sqrt{2} }$

$= \frac{4 + 2 \times \sqrt{2} }{3 + 2 \times \sqrt{2} }$

$= \frac{8 \times \sqrt{2} }{6 \times \sqrt{2} }$

$cutting \: \sqrt{2} \: by \: \sqrt{2}$

$= \frac{8}{6}$

$= \frac{4}{3}$

$so \: \frac{x + 1}{x} \: is \: rational$

♥️hope it will help you.♥️

Answer 2

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