Question

stiind ca ab+ac+bd+cd=√6+√15 si a+d=√5+√2 aratati ca b+c=√3

Answer 1

a(b+c)+d(b+c)=$\sqrt{6}+ \sqrt{15}$<=> (a+d)(b+c)=$\sqrt{6}+ \sqrt{15}$ <=>($\sqrt{5} + \sqrt{2})(b+c)$ =$\sqrt{6}+ \sqrt{15}$
b+c= $\frac{ \sqrt{6} + \sqrt{15} }{ \sqrt{5}+ \sqrt{2} }$
b+c= $\frac{ \sqrt{3} ( \sqrt{5} + \sqrt{2} )}{ \sqrt{5} + \sqrt{2} }$
Radical din 5 + radical din 2 se simpliifica<=> b+c= $\sqrt{3}<span>$.