Odpowiedź:
[tex]\sqrt{x}+\sqrt{x+6}=6\\\\(\sqrt{x}+\sqrt{x+6})^2=6^2\\\\(\sqrt{x})^2+2\sqrt{x}\cdot\sqrt{x+6}+(\sqrt{x+6})^2=36\\\\x+2\sqrt{x(x+6)}+x+6=36\\\\ x+2\sqrt{x^2+6x}+x+6=36\\\\2x+2\sqrt{x^2+6x}=36-6\\\\2x+2\sqrt{x^2+6x}=30\\\\2\sqrt{x^2+6x}=30-2x\ \ |:2\\\\\sqrt{x^2+6x}=15-x\\\\(\sqrt{x^2+6x})^2=(15-x)^2\\\\x^2+6x=15^2-2\cdot15x+x^2\\\\x^2+6x=225-30x+x^2\\\\x^2+6x+30x-x^2=225\\\\36x=225\ \ |:36\\\\x=\frac{225}{36}\\\\x=\frac{25}{4}\\\\x=6\frac{1}{4}[/tex]
