Question 1119680
Let K be {{{x}}} years old, then J be {{{(x+3)}}} years old,.
If you square K's age {{{(x^2)}}} and add twice J's age {{{2*(x+3)}}}, the result is {{{x^2+2*(x+3)}}} equal to {{{69}}}

{{{x^2+2*(x+3)=69}}}
{{{x^2+2x+6-69=0}}}
{{{x^2+2x-63=0}}}
{{{(x-7)(x+9)=0}}}
{{{x-7=0}}} or {{{x+9=0}}}
{{{x=7}}} or {{{x=-9}}} - it's an extraneous root (since it's negative)
K is {{{7 }}} years old and J is {{{7+3=10}}} years old