Question

If x+1/x=2 and x is real find the value of x^17+1/x^19?

Answer 1

Answer:

X+ 1/x = 2

Well its visible that x = 1 is satisfying above equation

1+1/1 = 1+1 = 2 as given

Or

x^2 +1 =>2x

x^2 - 2x +1= 0

(x-1)^2 = 0

x= 1

So, Put x= 1 in x^17 + 1/x^19

= 1+ 1/1

= 1+1

= 2

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Answer 2

$\underline \mathbb{SOLUTION}$

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

x = 1 satisfies above equation.

$= > 1 + \frac{1}{1 }$

$= > 1 + 1 = 2$

$\underline \mathbb{OR}$

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

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

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

$= > x = 1$

$\underline \mathbb{SO}$

$putting \: x = 1 \: in \: {x}^{17} + \frac{1}{ {x}^{19} }$

$= > 1 + \frac{1}{1}$

$= > 1 + 1$

$= > 2$

$\underline \mathbb{ANSWER= 2}$

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#BAL

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