点P(X,Y)是曲线3X^2 +4Y^2-6X-8Y-5=0上的点,则Z=X+2Y的最大最小值分别为

Z=X+2Y
x=z-2y
3X^2 +4Y^2-6X-8Y-5
=3(z-2y)^2+4y^2-6(z-2y)-8y-5
=16y^2+(4-12z)y+(3z^2-6z-5)
=0
△=(4-12z)^2-4*16(3z^2-6z-5)
=-48(z^2-6z-7)
=-48(z-7)(z+1)
≥0
(z-7)(z+1)≤0
-1≤z≤7
Z=X+2Y的最大值为7,最小值为-1