Question Number 90092 by jagoll last updated on 21/Apr/20
$$\mathrm{G}\left(\sqrt{\mathrm{x}+\mathrm{5}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{G}\left(\mathrm{x}^{\mathrm{2}} \right)\:=\:\mathrm{x}^{\mathrm{a}} −\mathrm{b} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b}\: \\ $$
Commented by john santu last updated on 21/Apr/20
$${set}\:\sqrt{{x}+\mathrm{5}}\:=\:{p}\:\Rightarrow\:{x}\:=\:{p}^{\mathrm{2}} −\mathrm{5} \\ $$$${G}\left({p}\right)\:=\:{p}^{\mathrm{2}} −\mathrm{5}\: \\ $$$${G}\left({x}^{\mathrm{2}} \right)\:=\:{x}^{\mathrm{4}} −\mathrm{5}\:\Rightarrow\begin{cases}{{a}\:=\:\mathrm{4}}\\{{b}\:=\:\mathrm{5}}\end{cases} \\ $$$$\therefore\:{a}+{b}\:=\:\mathrm{9}\: \\ $$