Question

. If (2-√3)/ (2+ √3) =a+b√3 then the value of a and b are?​

Answer 1

Answer:

a = 7, b = -4

Step-by-step explanation:

The reciprocal of 2-√2 is equal to​

$\frac{2 - \sqrt{3}}{2+ \sqrt{3} } \\= \frac{(2 - \sqrt{3})*(2 - \sqrt{3})} {(2 - \sqrt{3})(2 + \sqrt{3})}\\ = \frac{(2-\sqrt{3})^{2}}{2^2 - \sqrt{3}^{2} } \\=\frac{2^2 -2*2*\sqrt{3} + \sqrt{3}^2}{4 - 3}\\ = \frac{4 + 3 - 4\sqrt{3}}{1}\\ = 7 - 4\sqrt{3}$

According to the question:

$\frac{2 - \sqrt{3}}{2+ \sqrt{3} } \\ = a + b\sqrt{3}$

Hence,

$a + b\sqrt{3}\\ = 7 - 4\sqrt{3} \\ = 7 + (-4)\sqrt{3}$

So, after comparing both side we may write a = 7, b = -4

Answer 2

⇒A=7,B=4.

Step-by-step explanation:

This is how answers comes