`a) M=x^2-3x+10`
`\qquad M=x^2-2.x. 3/2+9/4+31/4`
`\qquad M=(x-3/2)^2+31/4>=31/4`
Dấu = xảy ra khi `x-3/2=0`
`<=> x=3/2`
Vậy `M_(min)=31/4<=>x=3/2`
`b) N=2x^2+5y^2+4xy+8x-4y-100`
`\qquad N=(x^2+4xy+4y^2)+(x^2+8x+16)+(y^2-4y+4)-120`
`\qquad N=(x+2y)^2+(x+4)^2+(y-2)^2-120>=-120`
Dấu = xảy ra khi `{(x+2y=0),(x+4=0),(y-2=0):}<=>{(x=-4),(y=2):}`
Vậy `N_(min)=-120<=>(x;y)=(-4;2)`
