Question

If x^2+1/x^2 = 27, find
1) x+1/x
2) x-1/x

Answer 1

Answer:

√29, 5

Step-by-step explanation:

ANSWER,

√29,. 5

ANSWER IS FOLLOW FOR QUESTIONS

Answer 2

★ Answer:-

1) We have,

[x + 1/x]² = x² + 2 × x × 1/x + 1/x²

=> [x + 1/x]² = x² + 2 + 1/x²

=> [x + 1/x]² = x² + 1/x² + 2

On substituting the value of x² + 1/x² from the question, we get,

[x + 1/x ]² = 27 + 2

=> [x + 1/x]² = 29

=> x + 1/x² = ±√29

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2) We have,

[x - 1/x]² = x² - 2 × x × 1/x + [1/x]²

=> [x -1/x]² = x² -2 + 1/x²

=> [x-1/x]² = x² + 1/x² -2

Substitute the value of x² + 1/x² from the question.

=> [x -1/x]² = 27 -2

=> [x -1/x]² = 25

=> [x -1/x]² = (±5)²

=> x -1/x = ± 5

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I hope this helps!❤