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Pavlova-9 [17]
3 years ago
11

The sum of the squares of three consecutive even integers is 980. Determine the integers.

Mathematics
2 answers:
olganol [36]3 years ago
4 0

Answer:

  16, 18, 20

Step-by-step explanation:

We can estimate that the square of the middle integer will be about 1/3 of 980. Then the middle integer is about ...

  √(980/3) ≈ 18.09

The integers are 16, 18, 20.

_____

<em>Check</em>

  16^2 +18^2 +20^2 = 256 +324 +400 = 980

viktelen [127]3 years ago
3 0

Answer:

16, 18, 20

Step-by-step explanation:

Let the three consecutive even integers be (x - 2), x, (x + 2)

\therefore \:  {(x -2 )}^{2}  +  {x}^{2}  + {(x + 2)}^{2}  = 980 \\  \therefore \:  {x}^{2}  - 4x + 4 +  {x}^{2}  + {x}^{2}   +  4x + 4  = 980 \\ \therefore \:  3{x}^{2}   + 8 = 980 \\ \therefore \:  3{x}^{2}  = 980 - 8 \\  \therefore \:  3{x}^{2}  = 972 \\  \\   \therefore \:  {x}^{2}  =  \frac{972}{3} \\  \\  \therefore \:  {x}^{2}  = 324 \\ \therefore \:   x =  \pm \sqrt{324}  \\  \therefore \:   x =  \pm \: 18 \\  \because \: x \: is \: even \: integer \\  \therefore \: x \neq  - 18 \\  \therefore \: x  =  18 \\  \\ x - 2 = 18 - 2 = 16 \\ x = 18 \\ x + 2 = 18 + 2 = 20 \\

Hence, three consecutive even integers are : 16, 18, 20.

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