Question

If x square + 1 by x square is equal to 27 then find the value of x + 1 by x and x - 1/x

Answer 1

Answer:

x - 1/x = ± 5

x + 1/x = ± √29

Step-by-step explanation:

Given :

x² + 1/x² = 27

⇒ x² + 1/x² + 2 = 27 + 2

⇒ x² + 1/x² + 2.x.1/x = 29

⇒ ( x + 1/x )² = 29

⇒ x + 1/x = ± √29

x² + 1/x² = 27

⇒ x² + 1/x² - 2 = 27 - 2

⇒ x² + 1/x² - 2.x.1/x = 25

⇒ ( x - 1/x )² = 25

⇒ ( x - 1/x ) = ± 5

Formulas used :

( a + 1/a )² = a² + 1/a² + 2

( a - 1/a )² = a² + 1/a² - 2

Answer 2

Answer:
x - 1/x = ± 5
x + 1/x = ± √29

Step-by-step explanation:

Given :

x² + 1/x² = 27
⇒ x² + 1/x² + 2 = 27 + 2
⇒ x² + 1/x² + 2.x.1/x = 29
⇒ ( x + 1/x )² = 29

⇒ x + 1/x = ± √29


x² + 1/x² = 27
⇒ x² + 1/x² - 2 = 27 - 2
⇒ x² + 1/x² - 2.x.1/x = 25
⇒ ( x - 1/x )² = 25

⇒ ( x - 1/x ) = ± 5


Formulas used :
( a + 1/a )² = a² + 1/a² + 2
( a - 1/a )² = a² + 1/a² - 2


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