\(a=\left(x-2\right)\left(x-4\right)\left(x^2-6x+10\right)\)
\(a=\left[x\left(x-4\right)-2\left(x-4\right)\right]\left(x^2-6x+10\right)\)
\(a=\left(x^2-4x-2x+8\right)\left(x^2-6x+10\right)\)
\(a=\left(x^2-6x+8\right)\left(x^2-6x+10\right)\)
\(a=\left(x^2-6x+9-1\right)\left(x^2-6x+9+1\right)\)
\(a=\left(x^2-6x+9\right)^2-1\ge-1\)
Dấu "=" xảy ra khi:
\(x^2-6x+9=0\)
\(\Rightarrow x^2-3x-3x+9=0\)
\(\Rightarrow x\left(x-3\right)-3\left(x-3\right)=0\)
\(\Rightarrow\left(x-3\right)^2=0\Leftrightarrow x=3\)
\(b=\dfrac{20}{60x-9x^2-21}\)
\(b=\dfrac{20}{-9x^2+60x-21}\)
\(b=\dfrac{20}{-\left(9x^2-60x+21\right)}\)
\(b=\dfrac{20}{-\left(9x^2-60x+100-79\right)}\)
\(b=\dfrac{20}{-\left(9x^2-60x+100\right)+79}\)
\(b=\dfrac{20}{-\left(3x-10\right)^2+79}\le-\dfrac{20}{79}\)
Dấu "=" xảy ra khi: \(x=\dfrac{10}{3}\)
