Question

5+2√3 by 7+4√3= a-b√3

Answer 1

hope this helps you ☺☺

Answer 2

Here is your answer...!!!!
First solve LHS

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(5 + 2√3 ) / ( 7 + 4√3 )
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Multiply by 7-4√3
Then we get

= (5 + 2√3 ) ( 7 - 4√3 ) / {( 7 + 4√3 ) ( 7 - 4√3 ) }

= { 5 ×7 - 5 × 4√3 + 2√3 × 7 - 2√3 × 4√3 } / { (7 )² - (4√3 )² }

above apply In the method
( x + y ) (x - y ) = x² - y²  
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= {35 -20√3 + 14√3 -24 } ÷ {49 - 48 }

= (11 - 6√3 )

therefore ,

LHS = RHS

11 - 6√3 = A - B√3

comparing both sides

A = 11
B/√3 =6/√3
B=6√3/ √3
B = 6
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Hope it's helpful