Question

Find the values of a and b:

√3 − 2
/√3 + 2= a + b√3​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{3} - 2}{ \sqrt{3} + 2 } = a + b \sqrt{3} \\ \\ lhs \: \\ \\ = \frac{ \sqrt{3} - 2 }{ \sqrt{3} + 2 } \times \frac{ \sqrt{3} - 2 }{ \sqrt{3} - 2} \\ \\ = \frac{ \sqrt{3} \times (\sqrt{3} - 2)\: - 2 \times ( \sqrt{3} - 2)}{ {2}^{2} - { (\sqrt{3)} }^{2} } \\ \\ = \frac{3 - 2 \sqrt{3} - 2 \sqrt{3} + 4}{4 - 3} \\ \\ = \frac{7 - 4 \sqrt{3} }{1} \\ \\ 7 - 4 \sqrt{3} = a + b \sqrt{3} \\ \\ a = 7\\ \\ b = - 4$