\(x^2-6x+3\)
\(=\left(x^2-6x+9\right)-6\)
\(=\left(x-3\right)^2-6\)
\(=\left(x-3+\sqrt{6}\right)\left(x-3-\sqrt{6}\right)\)
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a) \(x^2-6x+3\)
\(=x^2-2.x.3+9-6\)
\(=\left(x-3\right)^2-6\)
\(=\left(x-3\right)^2-\left(\sqrt{6}\right)^2\)
\(=\left(x-3+\sqrt{6}\right)\left(x-3-\sqrt{6}\right)\)
b) \(x^2-5x+14\)
\(=x^2-2.x\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2-\left(\dfrac{5}{2}\right)^2+14\)
\(=\left(x-\dfrac{5}{2}\right)^2-\dfrac{25}{4}+14\)
\(=\left(x-\dfrac{5}{2}\right)^2+\dfrac{31}{4}\)
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