Question

the question is find the value of a and b i) 5+2√3 upon7+4√3= a-6√3 ​

Answer 1

Answer:

$\bf \underline{Question}$

the question is find the value of a and b i) 5+2√3 upon7+4√3= a-6√3

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$\bf\underline{Given\to}$

(5 + 2√3 ) / ( 7 + 4√3 )=a-6√3

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$\bf \underline{To\: Find}$

• Find the value of a and b

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LHS = (5 + 2√3 ) / ( 7 + 4√3 )

rationalize the denominator

= (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 ]

Applying in the identity

( x + y ) (x - y ) = x² - y²  

Putting the all values:-

= [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 = 6