Đáp án:
`a)y=1`
`b)y=-5` hoặc `y=1`
Giải thích các bước giải:
`a)(y-2)³-(y-3)(y²+3y+9)+6(y+1)²=49`
`⇔y³-6y²+12y-8-(y³-27)+6(y²+2y+1)=49`
`⇔y³-6y²+12y-8-y³+27+6y²+12y+6=49`
`⇔(y³-y³)+(-6y²+6y²)+(12y+12y)+(-8+27+6)=49`
`⇔24y+25=49`
`⇔24y=49-25`
`⇔24y=24`
`⇔y=24:24`
`⇔y=1`
Vậy `y=1`
`b)(y+3)³-(y+1)³=56`
`⇔y³+9y²+27y+27-(y³+3y²+3y+1)=56`
`⇔y³+9y²+27y+27-y³-3y²-3y-1-56=0`
`⇔(y³-y³)+(9y²-3y²)+(27y-3y)+(27-1-56)=0`
`⇔6y²+24y-30=0`
`⇔6(y²+4y-5)=0`
`⇔y²+4y-5=0`
`⇔y²+5y-y-5=0`
`⇔y(y+5)-(y+5)=0`
`⇔(y+5)(y-1)=0`
`⇔`\(\left[ \begin{array}{l}y+5=0\\y-1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}y=-5\\y=1\end{array} \right.\)
Vậy `y=-5` hoặc `y=1`
