Question

If X²-2x+1=0 then x+1/x is equal to

Answer 1

x^2-x-x+1=0

x(x-1)-1(x-1)=0

(x-1)(x-1)=0

x=1 x=1

x+1/x

1+1/1=2

Answer 2

$\underline{\underline{\bold{\red{\: \: SOLUTION\: \:}}}}$➡

$\underline{ \bold{ \: Given \: : }} \: \: \: \: \: \: \: \: \: \: \bold{ x{}^{2} - 2x + 1 = 0 } \\ \\ \underline{ \bold{ \: To \: \: Find \: : }}\: \: \: \: \: \: \: \bold{x + \frac{ 1}{x} = ?}$

$\bold{x {}^{2} - 2x + 1 = 0 } \\ \\ \bold{ = > x {}^{2} - x - x + 1 = 0} \\ \\ \bold{ = > x(x - 1) - 1(x - 1) = 0} \\ \\ \bold{ = > (x - 1)(x - 1) = 0} \\ \\ \bold{So,} \\ \\ \bold{x - 1 = 0 \: \: = > x = 1} \\ \\ \bold{OR,} \\ \\ \bold{x - 1=0 \: \: = > x = 1 }$

$\bold{Now,} \\ \\ \bold{x + \frac{1}{x} = 1 + \frac{1}{1} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = \bold{1 + 1} \\ \\ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2}$


$\bold{Hence ,\: \: } \\ \\ \bold{If \: \: \boxed{ x {}^{2} - 2x + 1 = 0} \: \: then \: \: \boxed{x + \frac{1}{x } = 2 }}$

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✝$\mathfrak{\red{THANKS...}}$✝