Question

4(y+3)²=(y-2)² 用配方法解方程

Answer 1

4(y+3)²=(y-2)²
4(y²+6y+9)=y²-4y+4
4y²+24y+36-y²+4y-4=0
3y²+28y+32=0
3(y²+28/3*y)=-32
y²+28/3*y=-32/3
y²+28/3*y+196/9=-32/3+196/9
(y+14/3)²=100/9
所以y+14/3=10/3，或y+14/3=-10/3
所以y=-4/3，或y=-8

Answer 2

4(y+3)²=(y-2)²
4y²+24y+36-y²+4y-4=0
3y²+28y+32=0
3（y²+28/3y+196/9)-196/3+32=0
3(y+14/3)²-100/3=0
(y+14/3)²=100/9
y+14/3=±10/3
所以
y=-14/3±10/3
所以
y1==-4/3
y2=-8

Answer 3

[2(y+3)-(y-2)]*[2(y+3)+(y-2)]=0
(y+8)(3y+4)=0
y=-8或y=-4/3