Question

The sum of two numbers is 25 and the sum of their squares is 313

Answer 1

13
and
12

Step-by-step explanation:
If
x
+
y
=
25
then
y
=
25
−
x
.
Substitute:
x
2
+
y
2
=
313

x
2
+
(
25
−
x
)
2
=
313

2
x
2
−
50
x
+
312
=
0

x
2
−
25
x
+
156
=
0

(
x
−
13
)
(
x
−
12
)
=
0

x
=
13
,
y
=
12

x
=
12
,
y
=
13