Question

Rationalize 2+root 3 divide by 2-root 3=a+root 3find value of a and b

Answer 1

Hey friend,
Here is the answer you were looking for:
First of all,
I think you have a little mistake in your question i.e.
2+√3 / 2-√3 = a + b√3

Now,
Let's solve this:
$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{ {(2)}^{2} + ( \sqrt{3})^{2} + 2 \times 2 \sqrt{3} }{ {(2)}^{2} - ( \sqrt{3})^{2} } \\ \\ = \frac{4 + 3 + 4 \sqrt{3} }{4 - 3} \\ \\ = 7 + 4 \sqrt{3} \\ \\ 7 + 4 \sqrt{3} = a + b \sqrt{3} \\ so \: the \: value \: of \: a \: = 7 \: and \: b \: = 4$


Hope this helps!!!

@Mahak24

Thanks...
☺