If x-1-x-2- then find the positive value of -x-1-x-A- 2

The correct option is A 2Given: x + 1/x = 2 (√(x)+ 1/√(x))^2 = (√(x))^2 + (1/√(x))^2 + 2 √(x). 1/√(x) = x+1/x+2 =2+2 = 4 Hence, (√(x)+ 1/√(x))^2 = 4 Ta ...

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Standard IX

Mathematics

Algebraic Identities

If x+1/x=2, t...

Question

If $x + \frac{1}{x} = 2$ , then find the positive value of $\sqrt{x} + \frac{1}{\sqrt{x}}$ .
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Solution

The correct option is A 2
Given: $x + \frac{1}{x} = 2$

$(\sqrt{x} + \frac{1}{\sqrt{x}})^{2} = (\sqrt{x})^{2} + (\frac{1}{\sqrt{x}})^{2} + 2 \sqrt{x} . \frac{1}{\sqrt{x}} = x + \frac{1}{x} + 2 = 2 + 2 = 4$

Hence,

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

Taking square root on both the sides we get,

$\Rightarrow \sqrt{x} + \frac{1}{\sqrt{x}} = \sqrt{4} = 2$

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If x+1x=2 , then find the positive value of √x+1√x.2

The correct option is A 2Given: x+1x=2 (√x+1√x)2=(√x)2+(1√x)2+2√x.1√x=x+1x+2=2+2=4 Hence, (√x+1√x)2=4 Taking square root on both the sides we get, ⇒√x+1√x=√4=2

If $x + \frac{1}{x} = 2$ , then find the positive value of $\sqrt{x} + \frac{1}{\sqrt{x}}$ .
2