`8)`
`a,x^2-6x+10`
`=(x^2-6x+9)+1`
`=(x^2-2.x.3+3^2)+1`
`=(x-3)^2+1`
Do `(x-3)^2>=0AAx`
`→(x-3)^2+1>=1>0AAx`
Vậy `x^2-6x+10>0AAx`
`b,4x-x^2-5`
`=-x^2+4x-5`
`=-(x^2-4x+5)`
`=-[(x^2-4x+4)+1]`
`=-[(x^2-2.x.2+2^2)+1]`
`=-[(x-2)^2+1]`
`=-(x-2)^2-1`
Do `(x-2)^2>=0AAx`
`→-(x-2)^2<=0AAx`
`→-(x-2)^2-1<=-1<0AAx`
Vậy `4x-x^2-5<0AAx`
`9)`
`a,P=x^2-2x+5`
`=(x^2-2x+1)+4`
`=(x^2-2.x.1+1^2)+4`
`=(x-1)^2+4>=4AAx`
`->P_(min)=4`
Dấu "=" xảy ra `↔x-1=0↔x=1`
Vậy `P_(min)=4↔x=1`
`b,Q=2x^2-6x`
`=2(x^2-3x)`
`=2[(x^2-3x+9/4)-9/4]`
`=2[(x^2-2.x. 3/2+(3/2)^2)-9/4]`
`=2[(x-3/2)^2-9/4]`
`=2(x-3/2)^2-9/2>=-9/2AAx`
`->Q_(min)=-9/2`
Dấu "=" xảy ra `↔x-3/2=0↔x=3/2`
Vậy `Q_(min)=-9/2↔x=3/2`
`c,M=x^2+y^2-x+6y+10`
`=x^2+y^2-x+6y+1/4+3/4+9`
`=(x^2-x+1/4)+(y^2+6y+9)+3/4`
`=(x^2-2.x. 1/2+(1/2)^2)+(y^2+2.y.3+3^2)+3/4`
`=(x-1/2)^2+(y+3)^2+3/4>=3/4AAx;y`
`->M_(min)=3/4`
Dấu "=" xảy ra $↔\begin{cases}x-\dfrac{1}{2}=0\\y+3=0\end{cases}↔\begin{cases}x=\dfrac{1}{2}\\y=-3\end{cases}$
Vậy $M_{\min}=\dfrac{3}{4}↔\begin{cases}x=\dfrac{1}{2}\\y=-3\end{cases}$
