Question

Plz answer...Urgent....
$if \: x + \frac{1}{x} = 3 \\ find \: the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } ...plzzzz$

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Answer 1

The answer step by step is in the picture above.

Answer 2

Solution:

• Given : x + 1/x = 3

Find the value of x² + 1/x² ?

⇒ x² + 1/x² = ( x + 1/x)² - 2

⇒ x² + 1/x² = ( 3)² - 2

⇒ x² + 1/x² = 9 - 2

⇒ x² + 1/x² = 7

• Therefore, Required Value of x²+1/x² is 7.

Some important Identities:

• x² + 1/x² = ( x + 1/x)² - 2
• x² - 1/x² = ( x + 1/x)(x -1/x)
• x² - y² = ( x + y)(x - y)