Question Number 157752 by Engr_Jidda last updated on 27/Oct/21
$$ \\ $$$${A}\:{sum}\:{of}\:{two}−{digit}\:{number} \\ $$$${is}\:\mathrm{14}.\:{The}\:{tens}\:{digit}\:{is}\:{the}\:{square} \\ $$$${of}\:{a}\:{number}\:{which}\:{is}\:{two}\:{less}\:{than} \\ $$$${the}\:{unit}\:{digit}.\:{Find}\:{the}\:{two}−{digit}\:{numbers}. \\ $$
Answered by Rasheed.Sindhi last updated on 27/Oct/21
$${Required}\:{number}:\:\:\:\overline {\mathrm{tu}} \\ $$$$\mathrm{t}+\mathrm{u}=\mathrm{14}\Rightarrow\mathrm{t}=\mathrm{14}−\mathrm{u} \\ $$$$\mathrm{t}=\mathrm{v}^{\mathrm{2}} =\mathrm{u}−\mathrm{2} \\ $$$$\mathrm{t}=\mathrm{u}−\mathrm{2}=\mathrm{14}−\mathrm{u} \\ $$$$\:\:\:\mathrm{u}=\mathrm{8}\Rightarrow\mathrm{t}=\mathrm{8}−\mathrm{2}=\mathrm{6}\:\left(\mathrm{not}\:\mathrm{perfect}\:\mathrm{square}\right) \\ $$$$\mathcal{T}{he}\:{number}\:{is}\:\mathrm{68} \\ $$
Commented by Engr_Jidda last updated on 27/Oct/21
$${thanks} \\ $$