hi..
If x = rpot5-2, find x + 1/x, x2 + 1/x2
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Answers
Answered by
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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Answered by
7
Hi there!
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Refer to the attached picture for your answer.
If any doubt, ask freely.
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