Question

if x+1/x=2, then the value of x^102+1/x^102 is​

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

${x}^{102} + \frac{1}{ {x}^{102} }$

EVALUATION

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

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

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

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

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

$\implies \: x = 1$

So

${x}^{102} + \frac{1}{ {x}^{102} }$

$= {(1)}^{102} + \frac{1}{ {(1)}^{102} }$

$= 1 + 1$

$= 2$

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