Question Number 137645 by mey3nipaba last updated on 05/Apr/21
$${The}\:{sum}\:{of}\:{the}\:{squares}\:{of}\:{two}\:{consecutive} \\ $$$${odd}\:{numbers}\:{is}\:\mathrm{130}.\:{Find}\:{the}\:{larger}\:{number}. \\ $$
Answered by bemath last updated on 05/Apr/21
$${x}^{\mathrm{2}} +\left({x}+\mathrm{2}\right)^{\mathrm{2}} =\mathrm{130} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{126}=\mathrm{0} \\ $$$${x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{63}=\mathrm{0} \\ $$$$\left({x}+\mathrm{9}\right)\left({x}−\mathrm{7}\right)=\mathrm{0} \\ $$$$\begin{cases}{{x}=\mathrm{7}\:}\\{{x}+\mathrm{2}=\mathrm{9}\:\left({the}\:{larger}\:{number}\right)}\end{cases} \\ $$
Commented by mey3nipaba last updated on 05/Apr/21
$${yeah}.\:{thanks}\:{so}\:{much} \\ $$$$ \\ $$