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3 years ago

Let's say 2a, 2a + 2, 2a + 4 are three consecutive even numbers

Mathematics

1 answer:

Ede4ka [16]3 years ago

6 0

9514 1404 393

Answer:

4(3a^2 +6a +5)
a = 3, the numbers are 6, 8, 10

Step-by-step explanation:

1. The sum of squares is ...

(2a)^2 +(2a +2)^2 + (2a +4)^2 = 4a^2 +(4a^2 +8a +4) +(4a^2 +16a +16)

= 12a^2 +24a +20 . . . . . collect terms

= 4(3a^2 +6a +5) . . . . . . factor out 4

2. If the sum of the numbers is 24, we have ...

2a +(2a +2) +(2a +4) = 24

6a +6 = 24 . . . . . collect terms

a +1 = 4 . . . . . . . .divide by 6

a = 3 . . . . . . . subtract 1

2a = 6

2a +2 = 8

2a +4 = 10

The numbers are 6, 8, 10.

<em>Check</em>

The sum of squares is ...

4((a +2)(3a) +5) = 4(5(3·3) +5) = 4(50) = 200 . . . . as required

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