Question Number 148428 by 0731619 last updated on 27/Jul/21
Answered by Mathspace last updated on 27/Jul/21
$$\frac{\left({a}+{b}\right)^{\mathrm{2}} }{{ab}}−\mathrm{3}\:=\frac{\left({a}+{b}\right)^{\mathrm{2}} −\mathrm{3}{ab}}{{ab}} \\ $$$$=\frac{{a}^{\mathrm{2}} +\mathrm{2}{ab}+{b}^{\mathrm{2}} −\mathrm{3}{ab}}{{ab}} \\ $$$$=\frac{{a}^{\mathrm{2}} −{ab}+{b}^{\mathrm{2}} }{{ab}}=\frac{{a}^{\mathrm{2}} −\mathrm{2}{a}\frac{{b}}{\mathrm{2}}+\frac{{b}^{\mathrm{2}} }{\mathrm{4}}+{b}^{\mathrm{2}} −\frac{{b}^{\mathrm{2}} }{\mathrm{4}}}{{ab}} \\ $$$$=\frac{\left({a}−\frac{{b}}{\mathrm{2}\:}\right)^{\mathrm{2}} +\frac{\mathrm{3}{b}^{\mathrm{2}} }{\mathrm{4}}}{{ab}}>\mathrm{0} \\ $$$$ \\ $$