(5+√3)/(7-4√3) =a+b√3 , find the value of a and b class 9 maths

2 thoughts on “(5+√3)/(7-4√3) =a+b√3 , find the value of a and b class 9 maths”

1. Answer :-

   [tex]\implies\sf \dfrac{5+\sqrt3}{7-4\sqrt3} = a + b\sqrt3[/tex]

   Solving LHS :-

   [tex]\implies\sf \dfrac{5+\sqrt3}{7-4\sqrt3}[/tex]

   [tex]\implies\sf \dfrac{5+\sqrt3}{7-4\sqrt3} \times \dfrac{7+4\sqrt3}{7+4\sqrt3}[/tex]

   [tex]\implies\sf \dfrac{ (5+\sqrt3)(7+4\sqrt3)}{(7-4\sqrt3)(7+4\sqrt3)}[/tex]

   [tex]\implies\sf \dfrac{5( 7 + 4\sqrt3) + \sqrt3(7 + 4\sqrt3)}{ 7^2 – (4\sqrt3)^2}[/tex]

   [tex]\implies\sf \dfrac{35 + 20\sqrt3 + 7\sqrt3 + 4 \times 3}{49 – 48}[/tex]

   [tex]\implies\sf \dfrac{35 + 27\sqrt3 + 12}{1}[/tex]

   [tex]\implies\sf 47 + 27\sqrt3[/tex]

   Comparing with RHS :-

   [tex]\implies\sf 47 + 27\sqrt3 = a + b\sqrt3[/tex]

   • a = 47
   • b = 27

   Value of a = 47 and b = 27

   Reply

2. QuestioN :

   (5+√3)/(7-4√3) =a+b√3 , find the value of a and b

   GiveN :

   • (5+√3)/(7-4√3) =a+b√3

   To FiNd :

   • The value of a and b.

   ANswer :

   The value of a = 7 , b = – 3.

   SolutioN :

   √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

   ∴Hence, The value of a = 7 , b = – 3.

   _________________________

   Reply