Here,
x+y=12 and xy=22
[tex]\tt{(x+y)^2=x^2+y^2+2xy }[/tex] ⠀
according to the question,
[tex]\tt{ (12)^2=x^2+y^2+2×22 }[/tex] ⠀
[tex]\tt{ x^2+y^2=144-44 }[/tex] ⠀
[tex]\tt{x^2+y^2=100 }[/tex] ⠀
