Mỗi câu làm một ý nha :)
Giải:
a) \(F=x^2-8x+38\)
\(\Leftrightarrow F=x^2-8x+16+22\)
\(\Leftrightarrow F=\left(x-4\right)^2+22\ge22\)
\(\Leftrightarrow F_{Min}=22\)
\("="\Leftrightarrow x=4\)
b) \(C=-x^2-3x+5\)
\(\Leftrightarrow C=-x^2-3x-\dfrac{9}{4}+\dfrac{11}{4}\)
\(\Leftrightarrow C=-\left(x^2+3x+\dfrac{9}{4}\right)+\dfrac{11}{4}\)
\(\Leftrightarrow C=\dfrac{11}{4}-\left(x+\dfrac{3}{2}\right)^2\le\dfrac{11}{4}\)
\(\Leftrightarrow C_{Max}=\dfrac{11}{4}\)
\("="\Leftrightarrow x=-\dfrac{3}{2}\)
Vậy ...
a: \(Q=\left(x-1\right)^2+\left(x-3\right)^2\)
\(=x^2-2x+1+x^2-6x+9\)
\(=2x^2-8x+10\)
\(=2\left(x^2-4x+5\right)\)
\(=2\left(x-2\right)^2+2>=2\)
Dấu = xảy ra khi x=2
b: \(D=-2x^2+8x\)
\(=-2\left(x^2-4x+4-4\right)=-2\left(x-2\right)^2+8< =8\)
Dấu = xảy ra khi x=2
