1
\(A=x^2-8x+1=x^2-2.4x+16-15\\ =\left(x-4\right)^2-15\ge-15\)
Min A \(=-15\) khi \(x=4\)
2
\(B=x^2-3x+2=x^2-2.\dfrac{3}{2}+\dfrac{9}{4}-\dfrac{1}{4}\\ =\left(x-\dfrac{3}{2}\right)^2-\dfrac{1}{4}\ge-\dfrac{1}{4}\)
Min B \(=-\dfrac{1}{4}\) khi \(x=\dfrac{3}{2}\)
3
\(C=x^2+12x=x^2+2.6x+6^2-36\\=\left(x+6\right)^2-36\ge-36\)
Min C \(=-36\) khi `x=-6`
4
\(D=9x^2+12x-4\\ =\left(3x\right)^2+2.3x.2+2^2-8\\ =\left(3x-2\right)^2-8\ge-8\)
Min D \(=-8\) khi \(x=\dfrac{2}{3}\)
5
\(E=36x^2-60x+7=\left(6x\right)^2-2.6x.5+5^2-18\\ =\left(6x-5\right)^2-18\ge-18\)
Min E \(=-18\) khi \(x=\dfrac{5}{6}\)
6:
=y^2+y+1/4-1/4
=(y+1/2)^2-1/4>=-1/4
Dấu = xảy ra khi y=-1/2
7:
=5(x^2+4/5x-3/5)
=5(x^2+2*x*2/5+4/25-19/25)
=5(x+2/5)^2-19/5>=-19/5
Dấu = xảy ra khi x=-2/5
8: =7(x^2-12/7x-6/7)
=7(x^2-2*x*6/7+36/49-78/49)
=7*(x-6/7)^2-78/7>=-78/7
Dấu = xảy ra khi x=6/7
9: =x^2-2x+1+y^2-4y+4
=(x-1)^2+(y-2)^2>=0
Dấu = xảy ra khi x=1 và y=2
10: =x^2-x+1/4+1/4
=(x-1/2)^2+1/4>=1/4
Dấu = xảy ra khi x=1/2
