The sum of the squares of two consecutive positive even numbers is 340. The smallest number is
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Step-by-step explanation:
To find the answer, set up an equation.
Set
x
equal to the lower number, and
x
+
2
as the higher number since they are consecutive even numbers so they are two apart.
Now write out the equation according to the question
(
x
)
2
+
(
x
+
2
)
2
=
340
x
2
+
x
2
+
4
x
+
4
=
340
Combine like terms.
2
x
2
+
4
x
+
4
=
340
Set equal to zero so you can factor.
2
x
2
+
4
x
−
336
=
0
(
2
x
+
28
)
(
x
−
12
)
=
0
x
=
−
14
,
12
x
=
12
because the answer must be positive according to the question.
That means
x
+
2
is 14.
You can double check:
(
12
)
2
+
(
14
)
2
=
340
144
+
196
=
340
340
=
340
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