Đáp án :
`A=2057`
Giải thích các bước giải :
`C1:`
`A=a^2(a+1)-b^2(b-1)-11ab+2021`
`<=>A=a^3+a^2-b^3+b^2-11ab+2021`
`<=>A=(a^3-b^3)+(a^2-2ab+b^2)-9ab+2021`
`<=>A=(a-b)(a^2+ab+b^2)+(a-b)^2-9ab+2021`
`<=>A=3(a^2+ab+b^2)+(a-b)^2-9ab+2021`
`<=>A=3(a^2+ab-3ab+b^2)+(a-b)^2+2021`
`<=>A=3(a^2-2ab+b^2)+(a-b)^2+2021`
`<=>A=3(a-b)^2+(a-b)^2+2021`
`<=>A=3×3^2+3^2+2021`
`<=>A=27+9+2021`
`<=>A=2057`
`C2 :`
`a-b=3`
`<=>(a-b)^3=3^3`
`<=>a^3-b^3-3ab(a-b)=27`
`<=>a^3-b^3-9ab=27`
`+)A=a^2(a+1)-b^2(b-1)-11ab+2021`
`<=>A=a^3+a^2-b^3+b^2-11ab+2021`
`<=>A=(a^2-2ab+b^2)+(a^3-b^3-9ab)+2021`
`<=>A=(a-b)^2+(a^3-b^3-9ab)+2021`
`<=>A=3^2+27+2021`
`<=>A=9+27+2021`
`<=>A=2057`
Vậy `A=2057`
~Chúc bạn học tốt !!!~
