If x-3-22- show that x-1 x- 2-

We #160;have:x=3 22Now,1x=13 22 #215;3+223+22=3+2232 222=3+22 x+1x=3 22+3+22=6We #160;have:x 1x2=x+1x 2 #8658;x 1x2=6 2 #8658;x 1x2=4 Taking #160;th ...

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Standard XII

Mathematics

Method of Intervals

If x=3-22, sh...

Question

If $x = (3 - 2 \sqrt{2})$ , show that $(\sqrt{x} - \frac{1}{\sqrt{x}}) = \pm 2$ .

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Solution

$We have : x = 3 - 2 \sqrt{2} Now, \frac{1}{x} = \frac{1}{3 - 2 \sqrt{2}} \times \frac{3 + 2 \sqrt{2}}{3 + 2 \sqrt{2}} = \frac{3 + 2 \sqrt{2}}{3^{2} - {(2 \sqrt{2})}^{2}} = 3 + 2 \sqrt{2}$
$x + \frac{1}{x} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} = 6 We have : {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = x + \frac{1}{x} - 2 \Rightarrow {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = 6 - 2 \Rightarrow {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} = 4$
$Taking the square root of both sides, we get : \sqrt{x} - \frac{1}{\sqrt{x}} = \pm 2$

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If x=3-22, show that x-1x=±2.

We have:x=3-22Now,1x=13-22×3+223+22=3+2232-222=3+22 x+1x=3-22+3+22=6We have:x-1x2=x+1x-2⇒x-1x2=6-2⇒x-1x2=4 Taking the square root of both sides, we get:x-1x=±2

If $x = (3 - 2 \sqrt{2})$ , show that $(\sqrt{x} - \frac{1}{\sqrt{x}}) = \pm 2$ .