The smaller number is
3
(The other number is therefore
5
)
Step-by-step explanation:
We could use
x
and
y
to represent the two numbers, but it is possible to form an equation using only one variable.
If two numbers add up to 8, and we let one of them be
x
, the other one will be the difference, which is:
8
−
x
The sum of their squares is
34
x
2
+
(
8
−
x
)
2
=
34
←
(
a
−
b
)
2
=
a
2
−
2
a
b
+
b
2
x
2
+
64
−
16
x
+
x
2
=
34
2
x
2
−
16
x
+
64
−
34
=
0
2
x
2
−
16
x
+
30
=
0
←
÷
2
x
2
−
8
x
+
15
=
0
←
find factors of 15 which add to 8.
(
x
−
3
)
(
x
−
5
)
=
0
Setting factor equal to
0
gives:
x
=
3
and
x
=
5
Check:
3
+
5
=
8
3
2
+
5
2
=
9
+
25
=
34