Question Number 190878 by 073 last updated on 13/Apr/23
Answered by HeferH last updated on 13/Apr/23
$$\frac{\mathrm{a}}{\mathrm{b}}\:=\:\frac{\mathrm{c}}{\mathrm{d}}\:=\:\frac{\mathrm{e}}{\mathrm{f}}=\mathrm{k} \\ $$$$\:\mathrm{a}\:=\:\mathrm{bk} \\ $$$$\:\mathrm{e}\:=\:\mathrm{fk} \\ $$$$\:\mathrm{c}\:=\:\mathrm{dk} \\ $$$$\:\frac{\mathrm{bfk}^{\mathrm{2}} +\mathrm{d}^{\mathrm{2}} \mathrm{k}^{\mathrm{2}} }{\mathrm{bf}\:+\:\mathrm{d}^{\mathrm{2}} }\:=\:\mathrm{k}^{\mathrm{2}} \left(\frac{\mathrm{bf}+\mathrm{d}^{\mathrm{2}} }{\mathrm{bf}+\mathrm{d}^{\mathrm{2}} }\right)\:=\:\mathrm{k}^{\mathrm{2}} \:×\:\mathrm{1}\:=\:\mathrm{k}^{\mathrm{2}} \\ $$
Commented by 073 last updated on 13/Apr/23
$$\mathrm{nice} \\ $$