The three numbers are in the ratio 3 : 2 : 7.
Let the common multiplier be x.
The three numbers are:
First number =3x
Second number =2x
Third number =7x
The sum of their squares equals 558:
(3x)2+(2x)2+(7x)2=558
9x2+4x2+49x2=558
62x2=558
x2=62558
x2=9
x=3
The three numbers are:
First number =3x=3×3=9
Second number =2x=2×3=6
Third number =7x=7×3=21
Therefore, the three numbers are 9, 6, and 21 respectively.