Question

x²-mx+5=0
1/x1+1/x2=3
m=?

Answer 1

x²-mx+5=0
∆=m²-4·5=m²-20
x1,2=(m±√(m²-20) )/2

1/x1+1/x2=3
1/(m+√(m²-20))/2+1/(m-√(m²-20)/2=3
2/(m+√(m²-20))+2/m-√(m²-20))=3
2(m-√(m²-20))/(m+√(m²-20))(m-√(m²-20))+2(m+√(m²-20))/(m+√(m²-20))(m-√(m²-20))=3
(2m-2√(m²-20)+2m+2√(m²-20)) / (m²-m²-20)=3
4m/-20=3
m=3·(-20):4=-15