Question

if 1+2√3/2+√3=2a+b√3,where a and b are rational then the value of (a+b)2is

Answer 1

According to given sum,

$1 + 2 \sqrt{3} \div 2 + \sqrt{3} = 2a + b \sqrt{3}$

$1 + \sqrt{3} + \sqrt{3} = 2a + b \sqrt{3}$

$1 + 2 \sqrt{3} = 2a + b \sqrt{3}$

$2 \times1 \div 2 + 2 \sqrt{3} = 2a + b \sqrt{3}$

comparing the LHS and RHS. we get

a=1/2 and b= 2

(a+b)2

=(1/2+2)2

=2.5 (2)

=5

:-)hope it helps u.