Question

Stiind ca ab+ac+bd+cd=
\sqrt6+ \sqrt15 si a+d= \sqrt 5+ \sqrt2, aratati ca b+c= \sqrt3

Answer 1

$ab+ac+bd+cd= \sqrt{6} + \sqrt{15} \Leftrightarrow \\ \Leftrightarrow a(b+c)+d(b+c)= \sqrt{3}( \sqrt{2}+ \sqrt{5}) \Leftrightarrow \\\Leftrightarrow (b+c)(a+d)= \sqrt{3}( \sqrt{2}+ \sqrt{5}) \Leftrightarrow \\ \Leftrightarrow(b+c)( \sqrt{5}+ \sqrt{2})= \sqrt{3}( \sqrt{5}+ \sqrt{2})\Rightarrow \boxed{b+c= \sqrt{3}}.$