x-3-y-2-a-x-2-y-3-b-solve-for-x-y-a-b-R-

Question Number 119996 by behi83417@gmail.com last updated on 28/Oct/20

{\begin{cases} x^{3} + y^{2} = a \\ x^{2} + y^{3} = b \end{cases} [s o l v e f o r : x, y, a \neq b \in R]

Answered by TANMAY PANACEA last updated on 28/Oct/20

x^{6} = {(a - y^{2})}^{2}

x^{6} = {(b - y^{3})}^{3}

a^{2} - 2 {a y}^{2} + y^{4} = b^{3} - 3 b^{2} y^{3} + 3 {b y}^{6} - y^{9}

y^{9} - 3 {b y}^{6} + y^{4} + 3 b^{3} y^{3} - 2 {a y}^{2} - b^{3} = 0

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