Question

已知x+y=-8 xy=12 求{y倍[根号(x分之y)]}+{x倍[根号(y分之x)]

Answer 1

y*√(y/x)+x*√(x/y)
=-√[(y*√(y/x)+x*√(x/y))^2] (由题目知道x、y均为负数)
=-√[y^3/x+x^3/y+2xy]
=-√[(y^4+x^4)/xy+2*12]
=-√[(y^4+x^4)/12+24]
=-√[(((y+x)^2-2xy)^2-2x^2y^2)/12+24]
=-√[(((-8)^2-2*12)^2-2*12*12)/12+24]
=-√[(40^2-288)/12+24]
=-√[1312/12+24]
=-20√3/3

Answer 2

x+y=-8 xy=12
=y√y/x+x√x/y
=y√y^2/xy+x√x^2/xy
=y^2√1/xy+x^2√1/xy
=(x^2+y^2)√1/xy
=[(x+y)^2-2xy]√1/xy
=(64-24)*√1/12
=40*√3/6
=20√3/3

Answer 3

学会自己动脑呀 加油