Question

Calcule os valores de m para que:

2m-4 seja igual ao dobro de √m

Answer 1

$2m-4=2 \sqrt{m} \\ \frac{2m-4}{2} =m \\ (\frac{2m-4}{2})^{2}= (\sqrt{m})^{2} \\ \frac{(2m)^{2}-2.2m.4+4^{2}}{4} =m \\ \frac{4m^{2}-16m+16}{4} =m \\ m^{2}-4m+4-m=0 \\ m^{2}-5m+4=0 \\ \\ \Delta=(-5)^{2}-4.1.4 \\ \Delta=25-16 \\ \Delta=9 \\ \\ m'= \frac{-(-5)+ \sqrt{9}}{2.1} \\ m'= \frac{5+ 3}{2} \\ m'= \frac{8}{2} \\ m''= 4 \\ \\ m''= \frac{-(-5)- \sqrt{9}}{2.1} \\ m''= \frac{5-3}{2} \\ m''= \frac{2}{2} \\ m''= 1 \\ \\ \boxed {S=(1,4)}$