Question Number 216750 by sniper237 last updated on 17/Feb/25
$${If}\:\:{a}−{b}=\sqrt{{ab}}\:\:\:{find}\:\:\:{the}\:{value}\:{of}\:\frac{{a}−{b}}{{a}+{b}} \\ $$
Answered by mr W last updated on 17/Feb/25
$$\left({a}+{b}\right)^{\mathrm{2}} =\left({a}−{b}\right)^{\mathrm{2}} +\mathrm{4}{ab}={ab}+\mathrm{4}{ab}=\mathrm{5}{ab} \\ $$$$\Rightarrow{a}+{b}=\pm\sqrt{\mathrm{5}{ab}} \\ $$$$\Rightarrow\frac{{a}−{b}}{{a}+{b}}=\pm\frac{\sqrt{{ab}}}{\:\sqrt{\mathrm{5}{ab}}}=\pm\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\:\checkmark \\ $$