Math, asked by gf875edgh, 1 year ago

hi..


If x = rpot5-2, find x + 1/x, x2 + 1/x2


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Answers

Answered by BrainlyQueen01
9

Hey mate!


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Given :


x = √5 - 2


To find :


1) x + 1 / x


2) x² + 1 / x²


Solution :


x = √5 - 2


⇒ 1/x = 1/ √5 - 2


⇒ 1/x = 1/ √5 - 2 × √5 + 2/ √5 + 2


⇒ 1/x = √5 + 2 / (√5)² - (2)²


⇒ 1/x = √5 + 2 / 5 - 4


⇒ 1/x = √5 + 2


Now,


x + 1/x = √5 - 2 + √5 + 2


x + 1/x = 2√5


And, on squaring both sides,


( x + 1/x )² = (2√5) ²


⇒ x² + 1 / x² + 2 = 20


⇒ x² + 1 / x² = 20 - 2


⇒ x² + 1 / x² = 18.


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Thanks for the question !


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Answered by MsQueen
7

Hi there!


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Refer to the attached picture for your answer.


If any doubt, ask freely.


_______________________


Thanks for the question!


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