Question

Dau Coroana
Rezolvati ecuatia lg la patrat x -5lgx+6=0

Answer 1

Răspuns:

$C.E.:x>0\\Notam: lg\ x=t,\ t>0 \\Ecuatia\ devine: t^{2}-5t+6=0\\Delta=(-5)^{2}-4*6=25-24=1\\Delta>0 => Ecuatia\ are\ 2\ solutii => t_{1}=\frac{-(-5)+\sqrt{1} }{2}=3\ si\ t_{2}=\frac{-(-5)-\sqrt{1} }{2}=-3,\ dar\ t>0 => t=3 => lg\ x=3 => lg\ x=3*lg\ 10 => lg\ x=lg\ 10^{3} => x=10^{3}$