Question

x^2-9xy=28,3xy+9y^2=36求x-3y

Answer 1

x^2-9xy=28 (1)
3xy+9y^2=36 (2)
(1)+(2):
x^2-6xy+9y^2=28+36=64
(x-3y)^2=64
两边开平方：
x-3y=±8

Answer 2

解:方程组为x²-9xy=28，3xy+9y²=36；化为x²-9xy=28，xy+3y²=12，则3(x²-9xy)=

7(xy+3y²)，3x²-27xy=7xy+21y²，3x²-34xy-21y²=0，x=(17±4√22)y/3，有(17±4√22)y²+ 9y²=36，(26±4√22)y²=36，

y²=36/(√22±2)²，y=±6/(√22±2)，

y=±(√22±2)/3

∵x-3y=(17±4√22)y/3-3y=(8±4√22)y/3

∴x-3y=±(8+4√22)/3×(√22-2)/3或

±(8-4√22)/3×(√22+2)/3，x-3y=±8