Answer:
Suppose the two numbers are
a
and
b
"The sum of two numbers is 25" gives us:
a
+
b
=
25
"sum of their squares is 313" gives us:
a
2
+
b
2
=
313
From the first equation we have:
b
=
25
−
a
Substituting for
b
into the second we get:
a
2
+
(
25
−
a
)
2
=
313
∴
a
2
+
625
−
50
a
+
a
2
=
313
∴
2
a
2
−
50
a
+
312
=
0
∴
a
2
−
25
a
+
156
=
0
∴
(
a
−
12
)
(
a
−
13
)
=
0
∴
a
=
12
,
13
We now use the second equation to find the value of
b
corresponding to each solution.
a
=
12
⇒
b
=
25
−
12
=
13
a
=
13
⇒
b
=
25
−
13
=
12
So there is only one solution which is that the two numbers are
12
and
13
.
Step-by-step explanation:
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