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Question Number 173504 by AgniMath last updated on 12/Jul/22

Answered by behi834171 last updated on 12/Jul/22

A=(√x)+(1/( (√x)))⇒A^2 =x+(1/x)+2=4⇒A=2  .  ■

$${A}=\sqrt{{x}}+\frac{\mathrm{1}}{\:\sqrt{{x}}}\Rightarrow{A}^{\mathrm{2}} ={x}+\frac{\mathrm{1}}{{x}}+\mathrm{2}=\mathrm{4}\Rightarrow{A}=\mathrm{2}\:\:.\:\:\blacksquare \\ $$

Commented by Rasheed.Sindhi last updated on 12/Jul/22

Welcome Abu Behi sir after long time!

$${Welcome}\:\boldsymbol{{Abu}}\:\boldsymbol{{Behi}}\:\boldsymbol{{sir}}\:{after}\:{long}\:{time}! \\ $$

Commented by behi834171 last updated on 12/Jul/22

hello mr rasheed.thank you so much due   to warm welcome.mis you and all of  my dear friends and masters.  I′m here from now to much more times  after.

$${hello}\:{mr}\:{rasheed}.{thank}\:{you}\:{so}\:{much}\:{due}\: \\ $$$${to}\:{warm}\:{welcome}.{mis}\:{you}\:{and}\:{all}\:{of} \\ $$$${my}\:{dear}\:{friends}\:{and}\:{masters}. \\ $$$${I}'{m}\:{here}\:{from}\:{now}\:{to}\:{much}\:{more}\:{times} \\ $$$${after}. \\ $$

Answered by MJS_new last updated on 12/Aug/22

x+(1/x)=2 ⇔ x^2 −2x+1=0 ⇔ (x−1)^2 =0 ⇔ x=1  ⇒ answer is 2    x+(1/x)=a ⇒ (√x)+(1/( (√x)))=(√(a+2))

$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{2}\:\Leftrightarrow\:{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}=\mathrm{0}\:\Leftrightarrow\:\left({x}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{0}\:\Leftrightarrow\:{x}=\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{2} \\ $$$$ \\ $$$${x}+\frac{\mathrm{1}}{{x}}={a}\:\Rightarrow\:\sqrt{{x}}+\frac{\mathrm{1}}{\:\sqrt{{x}}}=\sqrt{{a}+\mathrm{2}} \\ $$

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