\sqrt{x-4} - \sqrt{6-x} = 2

ОДЗ: x-4>0         6-x>0          x>4            x<6 [latex]\sqrt{x-4}-\sqrt{6-x}=2\\\sqrt{x-4}=2+\sqrt{6-x}\\(\sqrt{x-4})^2=(2+\sqrt{6-x})^2\\x-4=4+4\sqrt{6-x}+6-x\\2\sqrt{6-x}=x-7\\(2\sqrt{6-x})^2=(x-7)^2\\4(6-x)=x^2-14x+49\\x^2-14x+49-24+4x=0\\x^2-10x+25=0\\(x-5)^2=0\\x-5=0\\x=5[/latex]