Question

if x=3+2√2 find the value of 1/x​

Answer 1

Answer:

$3 - 2 \sqrt{2}$

Step-by-step explanation:

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

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

Now rationalising the denominator

We get,

$\frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} }$

$= \frac{3 - 2 \sqrt{2} }{(3 + 2 \sqrt{2)}(3 - 2 \sqrt{2)} }$

{using identify (a+b)(a-b) = a²- b²}

$= \frac{3 - 2 \sqrt{2} }{ {(3)}^{2} - {(2 \sqrt{2})}^{2} }$

$= \frac{3 -2 \sqrt{2} }{9 - 4 \times 2}$

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

$= 3 - 2 \sqrt{2}$