#{((x-y)sqrty=sqrtx/2),((x+y)sqrtx=3sqrty):}#?

1 Answer
Cesareo R.
Jun 10, 2017

#((x,y),(-sqrt2,-1/sqrt2),(sqrt2,1/sqrt2),(-(3sqrt3)/4,-sqrt3/4),((3sqrt3)/4,sqrt3/4))#

Explanation:

#{(x-y=1/2 sqrt(x/y)),(x+y=3 sqrt(y/x)):}#

so

#{(x^2-y^2 = 3/2),((x-y)/(x+y)=1/6x/y):}#

Solving for #x,y# we get

#((x,y),(-sqrt2,-1/sqrt2),(sqrt2,1/sqrt2),(-(3sqrt3)/4,-sqrt3/4),((3sqrt3)/4,sqrt3/4))#

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