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Question Number 116538 by Khalmohmmad last updated on 04/Oct/20

x+(√y)=11  (√x)−y=24  x,y=?

$$\mathrm{x}+\sqrt{\mathrm{y}}=\mathrm{11} \\ $$$$\sqrt{\mathrm{x}}−\mathrm{y}=\mathrm{24} \\ $$$$\mathrm{x},\mathrm{y}=? \\ $$

Commented by mr W last updated on 04/Oct/20

no real solution!  x≥0, y≥0  x+(√y)=11 ⇒x≤11    24+y=(√x)≤(√(11))=3.3   ...(i)  24+y≥24   ...(ii)  (i) and (ii) are contradiction!

$${no}\:{real}\:{solution}! \\ $$$${x}\geqslant\mathrm{0},\:{y}\geqslant\mathrm{0} \\ $$$${x}+\sqrt{{y}}=\mathrm{11}\:\Rightarrow{x}\leqslant\mathrm{11} \\ $$$$ \\ $$$$\mathrm{24}+{y}=\sqrt{{x}}\leqslant\sqrt{\mathrm{11}}=\mathrm{3}.\mathrm{3}\:\:\:...\left({i}\right) \\ $$$$\mathrm{24}+{y}\geqslant\mathrm{24}\:\:\:...\left({ii}\right) \\ $$$$\left({i}\right)\:{and}\:\left({ii}\right)\:{are}\:{contradiction}! \\ $$

Commented by MJS_new last updated on 04/Oct/20

no solution in C

$$\mathrm{no}\:\mathrm{solution}\:\mathrm{in}\:\mathbb{C} \\ $$

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