Question

If x2 + 1/x2 = 27 ,find the values of each of the following:

i) x + 1/x ii) x- 1/x

Answer 1

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Given:

• x² + 1/x² = 27

We know that

• x² + 1/x² = (x+1/x)² - 2·x·1/x       [ a² + b² = (a+b)² - 2 ab ]

⇒ 27 = (x+1/x)² - 2

⇒ ( x+1/x)² = 29

∴  x + 1/x = √29

• x² + 1/x² = (x-1/x)² + 2·x·1/x   [a²+b² = (a-b)² + 2 ab]

⇒ 27 = (x-1/x)² + 2

⇒ (x-1/x )² = 25

∴  x - 1/x = ±5.

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Answer 2

Answer:

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