Question

5+√3/√7-4√3=a+7√b find a and b values

Answer 1

Hi ,

√7 + 4√3

= √7 + 2√ ( 4 × 3 )

= √( 4 + 3 ) + 2√( 4 × 3 )

Therefore ,

√7 + 4√3 = √4 + √3

= 2 + √3----( 1 )

LHS = ( 5 + √3 ) / ( √7 - 4√3 )

= ( 5 + √3 ) / ( 2 + √3 )

Rationalize the denominator

= (5+√3 )(2 -√3)/(2 + √3 ) ( 2-√3 )

= [10-5√3+2√3-3]/[( 2 )²- (√3)²]

= ( 7 - 3√3 )/(4 - 3 )

= 7 - 3√3

= RHS

7 - 3√3 = a + b√3

Compare both sides

a = 7 , b = - 3

I hope this helps you.

:)