Question Number 49823 by pieroo last updated on 11/Dec/18
$$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$
Answered by ajfour last updated on 11/Dec/18
$$\left({y}+\mathrm{4}\right)^{\mathrm{2}} ={y}^{\mathrm{2}} +\mathrm{8}{y}+\mathrm{16} \\ $$$$\Rightarrow\:\:\:\mathrm{9}{k}\:=\:\mathrm{16} \\ $$$$\Rightarrow\:\:\:{k}\:=\:\frac{\mathrm{16}}{\mathrm{9}}\:. \\ $$
Commented by pieroo last updated on 11/Dec/18
$$\mathrm{thanks}\:\mathrm{sir} \\ $$
Answered by peter frank last updated on 11/Dec/18
$$\mathrm{from} \\ $$$$\mathrm{b}^{\mathrm{2}} =\mathrm{4ac} \\ $$$$\mathrm{64}=\mathrm{36k} \\ $$$$\mathrm{k}=\frac{\mathrm{16}}{\mathrm{9}} \\ $$