Question

求解一道初三上册的数学题

先化简，再求值。
(6x根号x分之y +y分之3根号xy三次方)-(4x根号y分之x +根号36xy),其中x=1.5,y=27.

Answer 1

x=1.5﹥0, y=27﹥0
原式=[6x√(y/x)+(3/y)√(xy³)]-[4x√(x/y)+√(36xy)]
=6x√(y/x)+(3/y)√(xy³)-4x√(x/y)-√(36xy)
=6x√(xy/x²)+(3/y)×y√(xy)-4x√(xy/y²)-6√(xy)
=6x×√(xy)/x+3√(xy)-4x×√(xy)/y-6√(xy)
=6√(xy)+3√(xy)-4x√(xy)/y-6√(xy)
=3√(xy)-4x√(xy)/y
=[3y√(xy)-4x√(xy)]/y
=(3y-4x)√(xy)/y
=(3×27-4×1.5)√(1.5×27)/27
=(81-6)√(81/2)/27
=75√(81×2/2²)/27
=(25×9×1/2)×√2/9
=(25√2)/2

Answer 2

x﹥0, y﹥0
原式=[6x√(y/x)+(3/y)√(xy³)]-[4x√(x/y)+√(36xy)]
=6√(xy)+3√(xy)-4x√(xy)/y-6√(xy)
=3√(xy)-4x√(x/y)
=(3y-4x)√(x/y)
=(3×27-4×1.5)√(1.5/27)
=(81-6)√(1/18)=75/(3√2)
=(25√2)/2