Question

If a=2+root 3 /2-root 3and b =2-root 3/2+root 3then a+b is

Answer 1

Step-by-step explanation:

2+√3/2_√3=a+b√3

=(2+√3) *(2+√3) /(2-√3) *

(2+√3) =a+b√3

=(4+3+4√3) /(4-3) =a+b√3

=7+4√3=a+b√3

comparing on both sides we get

a=7

b=4

Answer 2

Step-by-step explanation:

$a = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \\ b = \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \\ a + b = \frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{ {( 2 + \sqrt{3}) ^{2} + {(2 - \sqrt{3} )}^{2} }^{} }{(2 - \sqrt{3})(2 + \sqrt{3} ) } \\ = \frac{4 + 4 \sqrt{3} + 3 + 4 - 4 \sqrt{3} + 3 }{4 - 3} \\ = \frac{4 + 3 + 4 + 3}{1} \\ = \frac{14}{1} \\ a + b = 14$