Question

if a is equal to 6 + 2 root 3 find the value of a minus one by a

Answer 1

Hey there!!

a = 6 + 2√3

a - ( 1 / a ) = ?

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1 / a = 1 / 6 + 2√3

( 1 ÷ 6 + 2√3 ) × ( 6 - 2√3 ÷ 6 - 2√3 )

In the denominators ,

Using the identity

( a + b ) ( a - b ) = a² - b²

( 6 - 2√3 ) ÷ ( 6 + 2√3 × 6 - 2√3 )

( 6 - 2√3 ) ÷ ( 36 - 12 )

( 6 - 2√3 ) ÷ ( 24 )

a - ( 1 ÷ a )

( 6 + 2√3 ) - ( 6 - 2√3 ÷ 24 )

[ 24 ( 6 + 2√3 ) - ( 6 - 2√3 ) ] ÷ 24

( 144 + 48√3 - 6 + 2√3 ) ÷ 24

( 138 - 50√3 ) ÷ 24

2 ( 69 - 25√3 ) ÷ ( 2 ) ( 12 )

69 - 25√3 ÷ 12

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ANS :-

( 69 - 25√3 ) / 12

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