x-y-1-3-x-3y-4-2x-3y-17-Find-x-and-y-

Question Number 141521 by 7770 last updated on 19/May/21

{\begin{cases} \sqrt[3]{x + y} + \sqrt{x - 3 y} = 4 \\ 2 x + 3 y = 17 \end{cases}

Find x and y .

Answered by MJS_new last updated on 20/May/21

{let}^{'} s try x + y = a^{3} \land x - 3 y = b^{2}

\Leftrightarrow

x = \frac{3 a^{3} + b^{2}}{4} \land y = \frac{a^{3} - b^{2}}{4}

a + b = 4 \Rightarrow b = 4 - a

9 a^{3} - b^{2} = 68 \Rightarrow a^{3} - \frac{1}{9} a^{2} + \frac{8}{9} a - \frac{28}{3} = 0 \Rightarrow a = 2

\Rightarrow b = 2

\Rightarrow x = 7 \land y = 1

Facebook Tweet Pin