Math, asked by thoisana3394, 1 year ago

Find a and b if 5+ root 3 / 7 - 4 root 3 = 94 a + 3 root 3 b

Answers

Answered by mickal
20
this is the solution...
Attachments:
Answered by pinquancaro
44

Answer:

The value of a=\frac{1}{2} and b=9

Step-by-step explanation:

Given : Expression \frac{5+\sqrt3}{7-4\sqrt3}=94a+3\sqrt{3}b

To find : The value of a and b?

Solution :

Solving the LHS of the expression,

\frac{5+\sqrt3}{7-4\sqrt3}              

Rationalize,

=\frac{5+\sqrt3}{7-4\sqrt3}\times \frac{7+4\sqrt3}{7+4\sqrt3}          

=\frac{(5+\sqrt3)(7+4\sqrt3)}{(7-4\sqrt3)(7+4\sqrt3)}        

=\frac{35+20\sqrt3+7\sqrt3+4\times 3}{7^2-(4\sqrt3)^2}        

=\frac{47+27\sqrt3}{49-48}  

=\frac{47+27\sqrt3}{1}      

=47+27\sqrt3      

On comparing with RHS,

47+27\sqrt3=94a+3\sqrt{3}b

94a=47

a=\frac{47}{94}

a=\frac{1}{2}

and 3b=27

b=\frac{27}{3}

b=9

Therefore, The value of a=\frac{1}{2} and b=9

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