Question

已知x,y为正数,且√x(√x+√y)=3√y(√x+5√y)

已知x,y为正数,且√x(√x+√y)=3√y(√x+5√y)求（2x+√xy+3y）\(x+√xy—y)的值

Answer 1

已知x,y为正数,且√x(√x+√y)=3√y(√x+5√y)已知x,y为正数,且√x(√x+√y)=3√y(√x+5√y)求（2x+√xy+3y）\(x+√xy—y)的值
√x(√x+√y)=3√y(√x+5√y)x+√xy=3√xy+15yx-2√xy-15y=0(√x-5√y)(√x+ 3√y)=0因为x,y为正数所以√x-5√y=0 √x=5√y
x=25y（2x+√xy+3y）\(x+√xy-y)=（50y+5y+3y）\(25y+5y-y)=58/29=2

Answer 2

√x(√x+√y)=3√y(√x+5√y)x+√(xy)=3√(xy)+15yx+√(xy)-3√(xy)-15y=0x-2√(xy)-15y=0(√x-5√y)(√x+ 3√y)=0因为x,y为正数所以√x-5√y=0 √x=5√y
x=25y（2x+√xy+3y）\(x+√xy-y)=（50y+5y+3y）\(25y+5y-y)=58/29=2

Answer 3

启发你一下啊已知的等式变形√x/√y=3(√x+5√y)/(√x+√y)令√x/√y=t 则 t=3(t+5)/(t+1) t=-3(舍） t=5（2x+√xy+3y）\(x+√xy—y)=(2t^2+t+3)/(t^2+t-1)= 把t代入就好啦

Answer 4

√x(√x+√y)=3√y(√x+5√y)x+√xy=3√xy+5yx-4√xy-5y=0(√x-5√y)(√x+√y)=0√x=5√y