Question

Subpunctul d) de la 15 va rog mult

Answer 1

$\it |z|=m+5 \Rightarrow |z|^2=(m+5)^2 \Rightarrow (m+1)^2+(3m-7)^2=(m+5)^2 \Rightarrow \\ \\ \Rightarrow m^2+2m+1+9m^2-42m+49=m^2+10m+25 \Rightarrow \\ \\ \Rightarrow 9m^2-50m+25=0 \Rightarrow 9m^2-45m-5m+25=0 \Rightarrow \\ \\ \Rightarrow 9m(m-5)-5(m-5)=0 \Rightarrow (m-5)(9m-5)=0 \Rightarrow \\ \\ \Rightarrow m_1=\dfrac{5}{9},\ \ m_2=5$