Răspuns:
[tex]\LARGE{x_{1}=3}\\\\\LARGE{x_{2}=2}[/tex]
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Pentru a calcula valoarea lui x, avem două metode:
Metoda I: Folosim formula ecuației de gradul al II-lea
[tex]x^2-5x+6=0\\\\\Delta = b^{2}-4ac\\\\a=1\\\\b=-5\\\\c=6\\\\\Delta = (-5)^{2}-4*1*6\\\\\Delta=25-24\\\\\Delta=1\\\\x_{1,2}=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x_{1,2}=\dfrac{5\pm\sqrt{1}}{2a}\\\\x_{1,2}=\dfrac{5\pm1}{2}\\\\x_{1}=\dfrac{5+1}{2}\\\\x_{1}=\dfrac{6}{2}\\\\\boxed{x_{1}=3}\\\\x_{2}=\dfrac{5-1}{2}\\\\x_{2}=\dfrac{4}{2}\\\\\boxed{x_{2}=2}[/tex]
Metoda a II-a: Descompunem x² - 5x + 6 cu suma și produsul.
x² - 5x + 6 =
x² - 2x - 3x + 6 =
x(x - 2) - 3(x - 2) =
(x - 3)(x - 2) = 0
x - 3 = 0
[tex]\boxed{x_{1}=3}[/tex]
x - 2 = 0
[tex]\boxed{x_{2}=2}[/tex]
