If \({\rm{x}} + \frac{1}{{\rm{x}}} = 5\), then find the value of \

1.	If \({\rm{x}} + \frac{1}{{\rm{x}}} = 5\), then find the value of \(\frac{{{{\left( {{\rm{x}} - {{\rm{x}}^{ - 1}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\)1. 42. 53. 64. 3
Answer» Correct Answer - Option 4 : 3 Given: \({\rm{x}} + \frac{1}{{\rm{x}}} = 5\) Formula used: \({\rm{a}} - \frac{1}{{\rm{a}}} = {\rm{\;}}\sqrt {{{\left( {{\rm{a}} + \frac{1}{{\rm{a}}}} \right)}^2} - 4}\) Calculation: \({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{{\left( {{\rm{x}} + \frac{1}{{\rm{x}}}} \right)}^2} - 4}\) ⇒ \({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{25} - 4}\) ⇒ \({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{21}}\) \({\rm{x}} + \frac{1}{{\rm{x}}} = 5\) ⇒ x² + 1 = 5x ⇒ 5x – x2 = 1 \(\frac{{{{\left( {{\rm{x}} - {{\rm{x}}^{ - 1}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\) ⇒ \(\frac{{{{\left( {{\rm{x}} - \frac{1}{{\rm{x}}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\) ⇒ {21/(1 + 6)} ⇒ 21/7 ⇒ 3 ∴ Required value is 3

If \({\rm{x}} + \frac{1}{{\rm{x}}} = 5\), then find the value of \(\frac{{{{\left( {{\rm{x}} - {{\rm{x}}^{ - 1}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\)1. 42. 53. 64. 3

Answer» Correct Answer - Option 4 : 3

Given:

\({\rm{x}} + \frac{1}{{\rm{x}}} = 5\)

Formula used:

\({\rm{a}} - \frac{1}{{\rm{a}}} = {\rm{\;}}\sqrt {{{\left( {{\rm{a}} + \frac{1}{{\rm{a}}}} \right)}^2} - 4}\)

Calculation:

\({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{{\left( {{\rm{x}} + \frac{1}{{\rm{x}}}} \right)}^2} - 4}\)

⇒ \({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{25} - 4}\)

⇒ \({\rm{x}} - \frac{1}{{\rm{x}}} = {\rm{\;}}\sqrt {{21}}\)

\({\rm{x}} + \frac{1}{{\rm{x}}} = 5\)

⇒ x² + 1 = 5x

⇒ 5x – x2 = 1

\(\frac{{{{\left( {{\rm{x}} - {{\rm{x}}^{ - 1}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\)

⇒ \(\frac{{{{\left( {{\rm{x}} - \frac{1}{{\rm{x}}}} \right)}^2}}}{{5{\rm{x}} - {{\rm{x}}^2} + 6}}\)

⇒ {21/(1 + 6)}

⇒ 21/7

⇒ 3

∴ Required value is 3