Question Number 184980 by Shrinava last updated on 15/Jan/23
$$\sqrt{\mathrm{7}}\:\:+\:\:\sqrt{\mathrm{6}}\:\:=\:\:\mathrm{a} \\ $$$$\sqrt{\mathrm{7}}\:−\:\sqrt{\mathrm{6}}\:=\:? \\ $$
Answered by SEKRET last updated on 15/Jan/23
$$\:\:×\:\begin{cases}{\sqrt{\mathrm{7}}\:+\:\sqrt{\mathrm{6}}\:\:=\:\boldsymbol{\mathrm{a}}}\\{\sqrt{\mathrm{7}}\:\:−\:\sqrt{\mathrm{6}}\:\:=\:\boldsymbol{\mathrm{x}}}\end{cases} \\ $$$$\:\:\:\boldsymbol{\mathrm{ax}}=\:\mathrm{1} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{x}}=\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}} \\ $$
Commented by Shrinava last updated on 15/Jan/23
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{ser}\:\mathrm{cool} \\ $$
Answered by aba last updated on 15/Jan/23
$$\sqrt{\mathrm{7}}−\sqrt{\mathrm{6}}=\frac{\left(\sqrt{\mathrm{7}}−\sqrt{\mathrm{6}}\right)\left(\sqrt{\mathrm{7}}+\sqrt{\mathrm{6}}\right)}{\:\sqrt{\mathrm{7}}+\sqrt{\mathrm{6}}}=\frac{\mathrm{7}−\mathrm{6}}{\mathrm{a}}=\frac{\mathrm{1}}{\mathrm{a}} \\ $$