Question

root 5 minus 2/root 5 + 2 the whole minus root 5 + 2 / root 5 minus 2 = a + root 5

Answer 1

Hi ,

LHS = ( √5 - 2 )/(√5 + 2 ) - (√5 + 2 )/( √5 -2 )

= [ ( √5 - 2 )² - ( √5 + 2 )² ]/[ (√5 +2 )(√5 -2 )]

= [ - 4 × ( √5 ) × 2 ] / [ ( √5 )² - 2² ]

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since ,

1 ) ( a - b )² - ( a + b )² = - 4ab

2 ) ( a + b ) ( a - b ) = a² - b²

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= ( - 8√5 )/ ( 5 - 4 )

= - 8√5

= 0 + ( - 8 )√5 -----( 1 )

= a + b√5 ----( 2 ) [ RHS given ]

Now , compare

( 1 ) & ( 2 ) , we get

a = 0 ,

b = -8

I hope this helps you.

: )