If \(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\) the

1.	If \(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\) then what will be the value of \(\frac{{\left( {x + \frac{1}{x}} \right)\; + \left( {{x^2} + \frac{1}{{{x^2}}}} \right)}}{2}\)1. 252. 273. 264. 23
Answer» Correct Answer - Option 2 : 27 Given: \(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\) Formula used: \({{\rm{a}}^2} + \frac{1}{{{{\rm{a}}^2}}} = {{\rm{c}}^2} - {\rm{\;}}2\) Calculation: \(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\) ⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}3^2 - 2\) ⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}9 - 2\) ⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}7\) ⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}7^2 - 2\) ⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}49 - 2\) ⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}47\) \(\frac{{\left( {x + \frac{1}{x}} \right)\; + \left( {{x^2} + \frac{1}{{{x^2}}}} \right)}}{2}\) ⇒ (7 + 47)/2 ⇒ 54/2 ⇒ 27 ∴ Required value is 27

If \(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\) then what will be the value of \(\frac{{\left( {x + \frac{1}{x}} \right)\; + \left( {{x^2} + \frac{1}{{{x^2}}}} \right)}}{2}\)1. 252. 273. 264. 23

Answer» Correct Answer - Option 2 : 27

Given:

\(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\)

Formula used:

\({{\rm{a}}^2} + \frac{1}{{{{\rm{a}}^2}}} = {{\rm{c}}^2} - {\rm{\;}}2\)

Calculation:

\(\sqrt {\rm{x}} + \frac{1}{{\sqrt {\rm{x}} }} = {\rm{\;}}3\)

⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}3^2 - 2\)

⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}9 - 2\)

⇒ \({\rm{x}} + \frac{1}{{{\rm{x}}}} = {\rm{\;}}7\)

⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}7^2 - 2\)

⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}49 - 2\)

⇒ \({\rm{x^2}} + \frac{1}{{{\rm{x^2}}}} = {\rm{\;}}47\)

\(\frac{{\left( {x + \frac{1}{x}} \right)\; + \left( {{x^2} + \frac{1}{{{x^2}}}} \right)}}{2}\)

⇒ (7 + 47)/2

⇒ 54/2

⇒ 27

∴ Required value is 27