If x be real and positive- then the value of y - x - 1-x satisfies

The correct option is C y ≥ 2 #160;Given y = x+ 1 / x =(√( x ) )^ 2 +( 1 /√( x ) #160; #160;) ^ 2 =( √( x ) 1 /√( x ) ...

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Standard IX

Mathematics

Absolute Value

If x be rea...

Question

If $x$ be real and positive, then the value of
$y = x + \frac{1}{x}$ satisfies

0 < y \leq 0.5

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0.5 < y \leq 1

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1 < y < 2

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y \geq 2

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Solution

The correct option is C $y \geq 2$
$G i v e n y = x + \frac{1}{x} = (\sqrt{x})^{2} + {(\frac{1}{\sqrt{x}})}^{2} = {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} + 2 \sqrt{x} \frac{1}{\sqrt{x}} = {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} + 2 F i r s t t e r m i s a s q u a r e d t e r m s o i t i s p o s i t i v e . ∴ {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} + 2 > 2 w h e n {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} h a s a f i n i t e v a l u e a n d {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} + 2 = 2 w h e n {(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2} i s z e r o . ∴ y \geq 2 (A n s)$

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If x be real and positive, then the value of y=x+1x satisfies

The correct option is C y≥2Giveny=x+1x=(√x)2+(1√x)2=(√x−1√x)2+2√x1√x=(√x−1√x)2+2Firsttermisasquaredtermsoitispositive.∴(√x−1√x)2+2>2when(√x−1√x)2hasafinitevalueand(√x−1√x)2+2=2when(√x−1√x)2iszero.∴y≥2(Ans)

If $x$ be real and positive, then the value of
$y = x + \frac{1}{x}$ satisfies