Question

4. Find the values of 'a' and 'b' in each of the
following:
(i)
2+√3/2-√3 = a +b√3​

Answer 1

Answer:

Step-by-step explanation:

2+√3/2-√3

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

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

so

a=7 , b= 4$\sqrt{3}$