$\text{Đáp án+Giải thích các bước giải:}$
`a) A=(x+y)³+x³=(x+y+x)[(x+y)²-x(x+y)+x²]`
`= (2x+y)(x²+2xy+y²-x²-xy+x²)`
`= (2x+y)(x²+xy+y²) `
Thay `2x+y=1 ⇒ (2x+y)(x²+xy+y²) =x²+xy+y²`
`b) B=x³-y³-3xy=(x-y)(x²+xy+y²)-3xy`
`#Sad`
`a)`
`A= (x+y)^3+x^3`
`= [(x+y)+x][(x+y)^2-x(x+y)+x^2]`
`= (x+y+x)(x^2+2xy+y^2-x^2-xy+x^2)`
`= (2x+y)(x^2+xy+y^2)`
`\text{→Thay}` `2x+y = 1` `\text{vào ta có:}`
`A= 1. (x^2+xy+y^2)`
`= x^2+xy+y^2`
`\text{→Áp dụng:}`
`+)` `A^3+B^3 = (A+B)(A^2-AB+B^2)`
`+)` `(A+B)^2 = A^2+2AB+B^2`
`b)`
`B= x^3-y^3-3xy`
`=(x^3-y^3)-3xy`
`= (x-y)(x^2+xy+y^2)-3xy`
`\text{→Áp dụng:}` `A^3-B^3 = (A-B)(A^2+AB+B^2)`
Cho `Δ ABC` nhọn,các đường cao `AD,BE,CF` cắt nhau tại` H` `a)` `CM:(HD)/(HA)+(HE)/(HB)+(HF)/(CH) ≥3/2` `CM:(HA)/(HD).(HB)/(HE).(HC)/(HF) ≥8`
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