Question

please solve the problem
I will give 15 thanks plus follow​

Answer 1

Answer :

x^2013 - 1/x^2012 = 0

Solution :

• Given : x + 1/x = 2
• To find : x^2013 - 1/x^2012 = ?

We have ;

=> x + 1/x = 2

=> (x² + 1)/x = 2

=> x² + 1 = 2x

=> x² - 2x + 1 = 0

=> (x - 1)² = 0

=> x - 1 = 0

=> x = 1

Now ,

=> x^2013 - 1/x^2012 = 1^2013 - (1/1)^2012

=> x^2013 - 1/x^2012 = 1 - 1

=> x^2013 - 1/x^2012 = 0

Hence ,

x^2013 - 1/x^2012 = 0

Answer 2

Question:

$If \:x + \frac{1}{x} = 2, \: then\: \: {x}^{2013} - \frac{1}{ {x}^{2012} } .$

To find:

$To \:find \: {x}^{2013} - \frac{1}{ {x}^{2012} } .$

Answer:

$\underline{ \sf \pink{\bf{ \: {x}^{2013} - \frac{1}{ {x}^{2012} } = 0}} \: }$

Given:

$\star \: x + \frac{1}{x} = 2$

Step-by-step explanation:

$\implies x + \frac{1}{x} = 2$

$\implies \frac{ {x}^{2} + 1 }{x} = 2$

$\implies {x}^{2} + 1 = 2x$

$\implies {x}^{2} - 2x + 1 = 0$

$Now \: factorisation,$

Product :- 1 = ( -1 ) × ( -1 )

Sum :- -2 = ( -1 ) + ( -1 )

$\implies {x}^{2} - x - x + 1 = 0$

$\implies x(x - 1) - 1(x - 1) = 0$

$\implies (x - 1)(x - 1) = 0$

$\implies {(x - 1)}^{2} = 0$

$\implies x - 1 = 0$

$\implies \boxed{x = 1}$

$\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

Now to find the value of ${x}^{2013} - \frac{1}{ {x}^{2012} }$

$Substitute \:the \:value\: of \:x,$

$\rightsquigarrow {(1)}^{2013} - \frac{1}{ {(1)}^{2012} }$

$\rightsquigarrow 1 - \frac{1}{1}$

$\rightsquigarrow 1 - 1$

$\rightsquigarrow \boxed{ {x}^{2013} - \frac{1}{ {x}^{2012} } = 0}$

$\therefore \underline{ \bf{ \: {x}^{2013} - \frac{1}{ {x}^{2012} } = 0} \: }$