Đáp án:
`↓↓`
Giải thích các bước giải:
`A =x^2+5y^2+4xy+2x+12`
`=x^2+2.x.(2y + 1) + (2y+1)^2 -(2y+1)^2+5y^2+12`
`=(x+2y+1)^2-4y^2-4y-1+5y^2+12`
`=(x+2y+1)^2+(y^2-4y+4) +7 `
`=(x+2y+1)^2+(y-2)^2 + 7 >= 7`
Dấu "=" xảy ra `⇔x=-5, y=2`
Vậy `A_(min)=7 <=> x=-5; y=2`
`---`
`B=x(x+2)(x+4)(x+6)+8`
`=[x(x+6)].[(x+2)(x+4)]+8`
`=(x^2+6x)(x^2+6x+8)+8`
Đặt `x^2+6x+4=a`
`=(a-4)(a+4)+8`
`=a^2-16+8=a^2-8>=-8`
Dấu "=" xảy ra `<=> a=0`
`<=> x^2+6x+4=0`
`<=> x^2+6x+9-5=0`
`<=> (x+3)^2-(\sqrt{5})^2=0`
`<=> (x+3-\sqrt{5})(x+3+\sqrt{5})=0`
`=>` \(\left[ \begin{array}{l}x=-3-\sqrt{5}\\x=\sqrt{5}-3\end{array} \right.\)
Vậy `B_(min)=-8 <=> x=-3-\sqrt{5}` hoặc `x=\sqrt{5}-3`
`----`
`C=(x+1)(2x-1)`
`=2x^2-x+2x-1=2x^2+x-1=2(x^2+1/2x-1/2)`
`=2(x^2+2. x. 1/4+1/16-1/16-1/2)`
`=2(x+1/4)^2-9/8>=-9/8`
Dấu "=" xảy ra `<=> x=-1/4`
Vậy `C_(min)=-9/8 <=> x=-1/4`
