设A=2x²-3XY+Y²,B=4X²-6XY-3Y²,且(X-5)和(Y+2)²是互为相反数,求3A-2B的值

问题描述:

设A=2x²-3XY+Y²,B=4X²-6XY-3Y²,且(X-5)和(Y+2)²是互为相反数,求3A-2B的值

(X-5)²和(Y+2)²是互为相反数
(X-5)²+(Y+2)²=0
(X-5)²=0,(Y+2)²=0
x=5
y=-2
3A-2B
=3(2x²-3XY+Y²)-2(4X²-6XY-3Y²)
=6x²-9XY+3Y²-8X²+12XY+6Y²
=6x²-8X²+12XY-9XY+3Y²+6Y²
=-2X²+3XY+9Y²
=-2*5²+3*5*(-2)+9*(-2)²
=-50-30+36
=-44

(X-5)和(Y+2)²是互为相反数
则|x-5|+(Y+2)²0
则x-5=0,Y+2=0
则x=5,Y=-2
3A-2B
=3(2x²-3XY+Y²)-2(4X²-6XY-3Y²)
=6x²-9XY+3Y²-8x²+12XY+6Y²
=-2x²+3XY+9Y³
=-2×25+3×(-10)+9×4
=-50-30+36
=-44