Question Number 137678 by otchereabdullai@gmail.com last updated on 05/Apr/21
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}=\mathrm{a}+\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} \\ $$
Commented by mr W last updated on 05/Apr/21
$${LHS}\:{is}\:{a}\:{function}!\:{you}\:{can}\:{not}\: \\ $$$${describe}\:{a}\:{function}\:{with}\:{a}\:{constant} \\ $$$${as}\:{your}\:{RHS}.\:{maybe}\:{you}\:{meant}: \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}={c}+\left(\mathrm{a}{x}+\mathrm{b}\right)^{\mathrm{2}} \:? \\ $$$${then} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}={x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}−\mathrm{9}=\left({x}−\mathrm{2}\right)^{\mathrm{2}} −\mathrm{9} \\ $$$$\Rightarrow{a}=\mathrm{1},\:{b}=−\mathrm{2},\:{c}=−\mathrm{9} \\ $$
Commented by otchereabdullai@gmail.com last updated on 10/Apr/21
$$\mathrm{exactly}\:\mathrm{prof}\:\mathrm{thanks}\:\mathrm{alot} \\ $$