1.将y=4x+4代入y=x²-2x-12,得x²-6x-16=0,解得x1=-2,x2=8,
S=(1/6)|x1-x2|³=1000/6=500/3
2.将y=4x+2m²代入y=x²-m²x-12,得x²-(m²+4)x-12-2m²=0
x1+x2=m²+4,x1x2=-12-2m²,
(x1-x2)²=(x1+x2)²-4x1x2=m⁴+16m²+64=(m²+8)²
|x1-x2|=m²+8
S(m)=(1/6)(m²+8)³
S'(m)=(1/2)(m²+8)•2m=m(m²+8),易知m>0时,S(m)为增函数,m