Question

(6+√3)/(7-4√3) = a + b√3

Answer 1

Step-by-step explanation:

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Answer 2

Answer :-

$\implies\sf \dfrac{6+\sqrt3}{7-4\sqrt3} = a + b\sqrt3$

Solving LHS :-

$\implies\sf \dfrac{6+\sqrt3}{7-4\sqrt3}$

Rationalizing the denominator :-

$\implies\sf \left(\dfrac{6+\sqrt3}{7-4\sqrt3}\right) \times \left(\dfrac{7+4\sqrt3}{7+4\sqrt3}\right)$

$\implies\sf \dfrac{(6+ \sqrt3)(7+4\sqrt3)}{(7+4\sqrt3)(7-4\sqrt3)}$

$\implies\sf \dfrac{6(7 + 4 \sqrt 3) + \sqrt3(7 + 4 \sqrt 3)}{7^2 - (4\sqrt3)^2}$

$\implies\sf \dfrac{42 + 24\sqrt3 + 7\sqrt3 + 4\times 3}{49-48}$

$\implies\sf \dfrac{42 + 12 + 31\sqrt3}{1}$

$\implies\sf 54 + 31\sqrt3$

Comparing LHS and RHS :-

$\implies\sf 54 + 31\sqrt3 = a + b\sqrt3$

• a = 54
• b = 31