If x -3-2 -2- then find the value of - x -1- x A- 1B- 2C- 3D- 4

The correct option is B 2 ( √(x) 1/√(x) )^2 = x + 1/x 2 put the value of x (3 + 2√(2)) + 1/(3+2√(2)) 2 = 3 + 2√(2) + 3 2√(2)/(3+2√(2))(3 2√(2)) 2 = 3 ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Surds

If x =3+2 √2,...

Question

If $x = 3 + 2 \sqrt{2}$ , then find the value of $(\sqrt{x} - \frac{1}{\sqrt{x}})$

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Solution

The correct option is B
$2$

${(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = x + \frac{1}{x} - 2$
put the value of $x$
$(3 + 2 \sqrt{2}) + \frac{1}{(3 + 2 \sqrt{2})} - 2 = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2}}{(3 + 2 \sqrt{2}) (3 - 2 \sqrt{2})} - 2 = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2}}{9 - 8} - 2 = 3 + 2 \sqrt{2} + \frac{3 - 2 \sqrt{2}}{1} - 2 = 3 + 2 \sqrt{2} + 3 - 2 \sqrt{2} - 2 = 6 - 2 = 4$
Since, ${(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = 4, (\sqrt{x} - \frac{1}{\sqrt{x}}) = 2$

Suggest Corrections

If x=3+2√2, then find the value of (√x−1√x)

The correct option is B 2 (√x−1√x)2=x+1x−2 put the value of x (3+2√2)+1(3+2√2)−2=3+2√2+3−2√2(3+2√2)(3−2√2)−2=3+2√2+3−2√29−8−2=3+2√2+3−2√21−2=3+2√2+3−2√2−2=6−2=4 Since, (√x−1√x)2=4,(√x−1√x)=2

If $x = 3 + 2 \sqrt{2}$ , then find the value of $(\sqrt{x} - \frac{1}{\sqrt{x}})$