Question Number 116512 by bounhome last updated on 04/Oct/20
$${give}\:{x}\in{R}\:{and}\:{prove}\:{that}\:{if}\:\:{x}=\sqrt{\mathrm{2}{x}+\mathrm{3}}\:{than}\:{x}=\mathrm{3} \\ $$
Commented by bemath last updated on 04/Oct/20
$$\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{3}=\mathrm{0}\:;\:\mathrm{x}\:\geqslant\mathrm{0} \\ $$$$\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{0}\Rightarrow\:\mathrm{x}\:=\:\mathrm{3} \\ $$