I have no idea how this equation: \(\displaystyle{\left({x}^{{2}}+{y}^{{2}}-{1}\right)}^{{3}}-{x}^{{2}}{y}^{{3}}={0}\)

calcolare45pj

calcolare45pj

Answered question

2022-03-31

I have no idea how this equation:
(x2+y21)3x2y3=0

Answer & Explanation

Alexzander Evans

Alexzander Evans

Beginner2022-04-01Added 9 answers

The solution set is obviously symmetric with respect to the y-axis. Therefore we may assume x0. In the domain [(x,y)R2x0] the equation is equivalent with
x2+y21=x23y
which can easily be solved for y:
y=12(x23±x43+4(1x2))
Now plot this, taking both branches of the square root into account. You might have to numerically solve the equation x43+4(1x2)=0 in order to get the exact x-interval.

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