Question

已知|x²-2xy-8y²|+2√x²-4xy+4y²-1=0,求3x+6y的值

Answer 1

即x²-2xy-8y²=0

x²-4xy+4y²-1=0

(x-4y)(x+2y)=0

且(x-2y)²=1

若x-4y=0

x=4y

则(4y-2y)²=1

y=±1/2

3x+6y=3*4y+6y=18y=±9

若x+2y=0

则原式=3(x+2y)=0

综上

原式=-9或9或0