Question

7-4 root 3/7+4 root 3 is equal to a+b root 3 find value a and b

Answer 1

This is the answer with complete solution
Enjoy..

Answer 2

Answer:

The value of a=97 and b=-56.        

Step-by-step explanation:

Given : $\frac{7-4\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$

To find : The value of a and b?

Solution :

We solve the given expression LHS by rationalizing,

$=\frac{7-4\sqrt{3}}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7+4\sqrt{3}}$

Applying property, $(a-b)(a+b)=a^2-b^2$

$=\frac{(7-4\sqrt{3})^2}{7^2-(4\sqrt{3})^2}$

$=\frac{49+48-56\sqrt3}{49-48}$

$=\frac{49+48-56\sqrt3}{1}$

$=97-56\sqrt3$

On comparing with RHS,

$a+b\sqrt{3}=97-56\sqrt3$

a=97 and b=-56

Therefore, The value of a=97 and b=-56.