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Grade 9Algebra

x + 1/x = 2
then x^37 + 1/x^23 = ?
tell me the answer please !!!!
as soon as possible......
difficult question

SAMBHAV MISHRA

8 Years agoGrade 9

1 Answer

Piyush Kumar Behera

Approved Tutor Answer8 Years ago

@Sambhav,In the question it is given that

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

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

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

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

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

Hence

$x-1=0$ is the only solution

so

$x=1$

So to find the value of

$x^{37}+\frac{1}{x^{23}}$

we can substitute $x=1$

so the answer is

$1^{37}+\frac{1}{1^{23}}=1$

So the answer is 1.Hope it helps.

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