If x -5-2 -6- then x -1- x -A- 5 - 4 -6- 5-2 -6D- 10

The correct option is D 10 x=5 2√(6) 1/x = 1/5 2√(6)×5+2√(6)/5+2√(6) =5+2√(6)/(5)^2 (2√(6))^2 =5+2√(6)/25 24 =5+2√(6) Therefore x+1/x=5 2̸√̸(̸6̸)̸+5+2̸√̸(̸6̸)̸ ...

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Byju's Answer

Standard IX

Mathematics

Expressing Recurring Decimal in p/q Form

If x =5-2 √6,...

Question

If $x = 5 - 2 \sqrt{6}$ , then $x + \frac{1}{x} =$ ___

$5$

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$4 \sqrt{6}$

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$5 + 2 \sqrt{6}$

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$10$

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Solution

The correct option is D
$10$

$x = 5 - 2 \sqrt{6}$

$\frac{1}{x} = \frac{1}{5 - 2 \sqrt{6}} \times \frac{5 + 2 \sqrt{6}}{5 + 2 \sqrt{6}}$

$= \frac{5 + 2 \sqrt{6}}{(5)^{2} - (2 \sqrt{6})^{2}}$

$= \frac{5 + 2 \sqrt{6}}{25 - 24}$

$= 5 + 2 \sqrt{6}$

Therefore $x + \frac{1}{x} = 5 - / 2 \sqrt{6} + 5 + / 2 \sqrt{6}$

$= 10$

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If x=5−2√6, then x+1x= ___

The correct option is D 10 x=5−2√6 1x=15−2√6×5+2√65+2√6 =5+2√6(5)2−(2√6)2 =5+2√625−24 =5+2√6 Therefore x+1x=5−/2√6+5+/2√6 =10

If $x = 5 - 2 \sqrt{6}$ , then $x + \frac{1}{x} =$ ___