Question

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Answer 1

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Answer 2

a² - 2 a = 1

⇒ a - 2  = 1/a

⇒ a - 1/a = 2 .... ( 1 )

( a - 1/a )² = 4

⇒ a² + 1/a² - 2 = 4

⇒ a² + 1/a² + 2 = 8

⇒ ( a + 1/a )² = 8

⇒ a + 1/a = 2√2 .........( 2 )

a² + 1/a² - 2 = 4

⇒ a² + 1/a² = 4 + 2 = 6 .............. ( 3 )

a² - 1/a² = ( a + 1/a )( a - 1/a )

= ( 2√2 )( 2 )

= 4√2 ...............( 4)