Question

if a and b are rational numbers and 2+√3/2-√3=a+b√3 find a and b​

Answer 1

Answer:

a=7

b=4

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{4 +4 \sqrt{3} + 3 }{4 - 3} \\ = \frac{7 + 4 \sqrt{3} }{1} \\ = 7 + 4 \sqrt{3} \\ a + b \sqrt{3} = 7 + 4 \sqrt{3} \\ a = 7 \\ b = 4$

Answer 2

Answer:

Step-by-step explanation:

2+root3/2-root 3

=2+$\sqrt{3$/2-$\sqrt{3$ * 2+$\sqrt{3$/2-$\sqrt{3$

=(2+$\sqrt{3$)^2/ 2^2 - ($\sqrt{3$)^2

4+3+4$\sqrt{3$/4-3

7+4$\sqrt{3$/1

On comparing

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

Hence a = 7

b = 4