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Question Number 139799 by Study last updated on 01/May/21

$$x+\sqrt{y}=11$$$$\sqrt{x}+y=7$$$$x=?y=?$$

Commented by MJS_new last updated on 01/May/21

$$x⩾0\wedge y⩾0$$$$x=p^2\wedge y=q^2$$$$p^2+q=11\Rightarrow q=11-p^2$$$$p+q^2=7\to p^4-22p^2+p+114=0$$$$(p-3)(p^3+3p^2-13p-38)=0$$$$p_1=3\Rightarrow q_1=2\Rightarrow x_1=9\wedge y_1=4$$$$p^3+3p^2-13p-38=0$$$$\mathrm{this}\mathrm{has}3\mathrm{real}\mathrm{solutions}\mathrm{but}\mathrm{they}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{solve}$$$$\mathrm{the}\mathrm{given}\mathrm{system}\mathrm{of}\mathrm{equations}$$

Answered by bramlexs22 last updated on 01/May/21

$$\{\begin{array}{l}\mathrm{x}=9\\ \mathrm{y}=4\end{array}$$

Commented by Study last updated on 01/May/21

$$whatisthepractice?$$

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