0\\x_1-x_2=2\sqrt{5}\\\\D=(-12)^2-4n=144-4n\\144-4n>0\\4n<144\\n<36\\\\x_{1,2}=\frac{12б\sqrt{144-4n}}{2}\\\\\frac{12+\sqrt{144-4n}}{2}-\frac{12-\sqrt{144-4n}}{2}=2\sqrt{5}|*2\\\\12+\sqrt{144-4n}-12+\sqrt{144-4n}=4\sqrt{5}\\2\sqrt{144-4n}=4\sqrt{5}|:2\\\sqrt{144-4n}=2\sqrt{5}\\144-4n=20\\4n=124\\n=31" alt="x^2-12x+n=0\\D>0\\x_1-x_2=2\sqrt{5}\\\\D=(-12)^2-4n=144-4n\\144-4n>0\\4n<144\\n<36\\\\x_{1,2}=\frac{12б\sqrt{144-4n}}{2}\\\\\frac{12+\sqrt{144-4n}}{2}-\frac{12-\sqrt{144-4n}}{2}=2\sqrt{5}|*2\\\\12+\sqrt{144-4n}-12+\sqrt{144-4n}=4\sqrt{5}\\2\sqrt{144-4n}=4\sqrt{5}|:2\\\sqrt{144-4n}=2\sqrt{5}\\144-4n=20\\4n=124\\n=31" align="absmiddle" class="latex-formula">