Question

if 5-root3/2+root3=x+y root3 then x=

Answer 1

$\frac{ 5 - \sqrt{3} }{2 + \sqrt{3} } = x + y \sqrt{3} \\ \\ \frac{5 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = x + y \sqrt{3} \\ \\ \frac{10 - 5 \sqrt{3} - 2 \sqrt{3} + 3 }{4 - 3} = x + y \sqrt{3} \\ \\ 13 - 7 \sqrt{3} = x + y \sqrt{3} \\ \\ comparing \: both \: sides \: we \: get \\ x = 13 \\ y = - 7$