`#AkaShi`
`a) M=x^2-3x+10`
`M=x^2-3x+9/4+31/4`
`M=(x^2-2*3.2*x+9/4)+31/4`
`M=(x-3/2)^2+31/4`
Ta có: `(x+3/2)^2 >= 0 ∀ x`
`⇔(x+3/2)^2 +31/4 >= 31/4`
Dấu `"="` xảy ra khi `(x-3/2)^2=0⇔x=3/2`
Vậy $Min_{M}=31/4$ khi `x=3/2`
....................
`a) N=2x²+5y²+4xy+8x-4y-100`
`N=x²+x²+4y²+y²+4xy+8x-4y-120+16+4`
`N=(x²+4xy+4y²)+(y²-4y+4)+(x²+8x+16)-120`
`N=(x+2y)²+(y-2)²+(x+4)²-120`
Ta có:
`(x+2y)² >= 0 ∀ x`
`(y-2)² >= 0 ∀ x`
`(x+4)² >= 0 ∀ x`
`⇔(x+2y)²+(y-2)²+(x+4)²-120 >= -120`
Dấu `"="` xảy ra khi :
`(y-2)^2=0⇔y=2`
`(x+4)^2=0⇔x=-4`
Vậy $Min_{N}=-120$ khi `x=-4;y=2`
