If x-2-3 then x-1-x equals a -2-3 b 2 c 4 d 4-2-3

X=2+√(3) 1/x = 1/2+√(3) = 1(2 √(3))/(2+√(3))(2 √(3)) = 2 √(3)/4 3 = 2 √(3)/1 = 2 √(3) ( x+1/x ) = 2+√(3) +2 √(3) = 4 Hence, the correct answer is option ( ...

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Standard IX

Mathematics

Rationalisation

If x=2+√3 the...

Question

If $x = 2 + \sqrt{3}$ then $(x + \frac{1}{x})$ equals

(a) $- 2 \sqrt{3}$ (b) 2 (c) 4 (d) $4 - 2 \sqrt{3}$

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Solution

$x = 2 + \sqrt{3} \frac{1}{x} = \frac{1}{2 + \sqrt{3}} = \frac{1 (2 - \sqrt{3})}{(2 + \sqrt{3}) (2 - \sqrt{3})} = \frac{2 - \sqrt{3}}{4 - 3} = \frac{2 - \sqrt{3}}{1} = 2 - \sqrt{3} (x + \frac{1}{x}) = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$

Hence, the correct answer is option (c)

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If x=2+√3 then (x+1x) equals (a) −2√3 (b) 2 (c) 4 (d) 4−2√3

x=2+√31x=12+√3=1(2−√3)(2+√3)(2−√3)=2−√34−3=2−√31=2−√3(x+1x)=2+√3+2−√3=4 Hence, the correct answer is option (c)

If $x = 2 + \sqrt{3}$ then $(x + \frac{1}{x})$ equals

(a) $- 2 \sqrt{3}$ (b) 2 (c) 4 (d) $4 - 2 \sqrt{3}$

$x = 2 + \sqrt{3} \frac{1}{x} = \frac{1}{2 + \sqrt{3}} = \frac{1 (2 - \sqrt{3})}{(2 + \sqrt{3}) (2 - \sqrt{3})} = \frac{2 - \sqrt{3}}{4 - 3} = \frac{2 - \sqrt{3}}{1} = 2 - \sqrt{3} (x + \frac{1}{x}) = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$

Hence, the correct answer is option (c)