Question

If x = 3 - 2√2 , find x +1/x

Answer 1

✑ Given

If x = 3 - 2√2 , find x +1/x

✑ To find

Find the value of x + 1/x

✑ Solution

• x = 3 - 2√2

Then,

➡ 1/x = 1/3 - 2√2

★ Rationalize it

➡ 1/x = 1/3 - 2√2 × 3 + 2√2/3 + 2√2

➡ 1/x = 3 + 2√2/(3)² - (2√2)²

➡ 1/x = 3 + 2√2/9 - 8

➡ 1/x = 3 + 2√2

Now, the value of x + 1/x

• 1/x = 3 + 2√2

➡ x + 1/x

➡ 3 - 2√2 + 3 + 2√2

➡ 3 + 3

➡ 6

Answer 2

✰Answer✰

☛Given:

• $\large{ \sf{x = 3 - 2 \sqrt{2} }}$

☛To find:

• $\large{ \sf{x + \frac{1}{x} }}$

✰Solution✰

$\large{ \sf{ \rightarrow x = 3 - 2\sqrt{2} } } \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } }}$

☛By rationalising the denominator,

$\large{ \sf{ \green{ \rightarrow \: rationalising \: factor \: of \: 3 - 2 \sqrt{2} = 3 + 2 \sqrt{2} }}} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{(3 - 2 \sqrt{2})(3 + 2 \sqrt{2} ) } }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{( {3}^{2} - {(2 \sqrt{2}) }^{2} )} }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8} }} \\ \\ \large{ \sf{ \rightarrow \: \frac{1}{x} = 3 + 2 \sqrt{2} }}$

☛Now adding x + 1/x to get required result,

$\large{ \sf{ \rightarrow \: x + \frac{1}{x} = 3 - \cancel{2 \sqrt{2} }+ 3 + \cancel{2 \sqrt{2}} }} \\ \\ \large{ \sf{ \rightarrow \: \boxed{ \purple{x + \frac{1}{x} = 6}}}}$

✰So Final Answer✰

$\large{ \boxed{ \bf{ = 6}}}$