Question

x2 +1/x2 = 23 find the values of x+1/x
​

Answer 1

the values of x+1/x = 5

Step-by-step explanation:

$\\ \tt \large \purple {Given}$

• x² + 1/x² = 23

$\\ \tt \large \purple{To \: find}$

• find the values of x+1/x .

$\: \\ \tt \large \purple {Formula \: used} \:$

$\boxed{ \sf \: {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy}$

$\tt \large \purple{Solution}$

$\boxed{ \sf \: {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy}$

$\\ \bf \: use \: Formula \: \boxed{ \sf \: {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy} \\ \\ :\implies\sf \: {\big(x + \dfrac{1}{x}\big )}^{2} - 2 \times x \times \dfrac{1}{x} = 23 \\ \\ :\implies \sf \: {\big(x + \dfrac{1}{x}\big )}^{2} - 2\times \cancel x \times \dfrac{1}{ \cancel x} \\ \\ :\implies\sf \: {\big(x + \dfrac{1}{x}\big )}^{2} - 2 = 23 \\ \\ :\implies \sf \: {\big(x + \dfrac{1}{x}\big )}^{2} = 23 + 2 \\ \\ :\implies \sf \: {\big(x + \dfrac{1}{x}\big )}^{2} = 25 \\ \\ :\implies\sf \: x + \dfrac{1}{x} = \sqrt{25} \\ \\ :\implies \sf \: x + \dfrac{1}{x} = 5$

Hence, required values of x+1/x is 5 .

★ Some basic identities :-

• ( a + b )² = a² + ab + b² .
• ( a – b )² = a² – ab + b² .
• ( a + b ) ( a – b ) = a² – b² .
• ( a + b )³ = a³ + b³ + 3ab( a + b )
• ( a – b )³ = a³ – b³ – 3ab( a – b )
• ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca .