9: \(I=2x^2+4x+3\)
\(=2\left(x^2+2x+\dfrac{3}{2}\right)\)
\(=2\left(x^2+2x+1+\dfrac{1}{2}\right)\)
\(=2\left(x+1\right)^2+1>=1\forall x\)
Dấu '=' xảy ra khi x+1=0
=>x=-1
10: \(K=4x^2+3x+2\)
\(=\left(2x\right)^2+2\cdot2x\cdot\dfrac{3}{4}+\dfrac{9}{16}+\dfrac{23}{16}\)
\(=\left(2x+\dfrac{3}{4}\right)^2+\dfrac{23}{16}>=\dfrac{23}{16}\forall x\)
Dấu '=' xảy ra khi \(2x+\dfrac{3}{4}=0\)
=>\(2x=-\dfrac{3}{4}\)
=>\(x=-\dfrac{3}{8}\)
11: \(M=\left(x-1\right)\left(x-3\right)+11=x^2-4x+3+11\)
\(=x^2-4x+4+10=\left(x-2\right)^2+10>=10\forall x\)
Dấu '=' xảy ra khi x-2=0
=>x=2
12: \(N=\left(x-3\right)^2+\left(x-2\right)^2\)
\(=x^2-6x+9+x^2-4x+4\)
\(=2x^2-10x+13=2\left(x^2-5x+\dfrac{13}{2}\right)\)
\(=2\left(x^2-2\cdot x\cdot\dfrac{5}{2}+\dfrac{25}{4}+\dfrac{1}{4}\right)=2\left(x-\dfrac{5}{2}\right)^2+\dfrac{1}{2}>=\dfrac{1}{2}\forall x\)
Dấu '=' xảy ra khi x-5/2=0
=>x=5/2
