Question

-4x²y/3

已知4x^2+y^2-4x-6y+10=0,求（2/3x√9x+y^2√x/y^3）-(x^2√1/x-5x√y/x)的值

Answer 1

4x^2+y^2-4x-6y+10=0
4x²-4x+1+y²-6y+9=0
(2x-1)²+(y-3)²=0
∴2x-1=0 y-3=0
解得x=1/2 y=3
（2/3x√9x+y^2√x/y^3）-(x^2√1/x-5x√y/x)
=2x√x+√xy-x√x+5√xy
=x√x+6√xy
=1/2√(1/2)+6√(1/2*3)
=√2/4+3√6