Question

if x - 1/x = 1 find x^2 - 1/x^2 ???​

Answer 1

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$x - \frac{1}{x} = 1$

square both sides

${(x - \frac{1}{x} )}^{2} = {(1)}^{2}$

${x}^{2} - 2.x. \frac{1}{x} + \frac{1}{ {x}^{2} } = 1$

${x}^{2} + \frac{1}{ {x}^{2} } = 1$

Answer 2

Question:

• If x - 1/x = 1 then find the value of x² - 1/x²

Given:

• x - 1/x = 1.....(I)

To find:

• x² - 1/x² = ?

Solution:

• x - 1/x = 1

( By squaring both sides)

=> (x - 1/x )² = (1)²

=> x² - 2 × x × 1/x + 1/x² = 1

=> x² - 2 + 1/x² = 1

=> x² + 1/x² = 1 + 2

=> x² + 1/x² = 3

• Now, x² + 1/x² = 3

=> x² + 1/x² + 2 × x × 1/x = 3 + 2

( We added 2 from both side, so there will be no change and x will be cancelled)

=> (x + 1/x)² = 5

( By using (a + b)² = a² + 2ab + b² )

=> x + 1/x = √5 ..(II)

• We have,

x² - 1/x² = (x + 1/x) ( x - 1/x)

=> x² - 1/x² = ( √5 )( 1 )

( Putting values of x - 1/x and x + 1/x from (I) and (II))

=> x² - 1/x² = √5

Answer:

• x² - 1/x² = √5