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2 years ago

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

Mathematics

2 answers:

olganol [36]2 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]2 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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lys-0071 [83]

Answer:

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Step-by-step explanation:

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Now we can cancel the h in the numerator and denominator under the assumption that h is not 0.

$= \dfrac{-1}{x(x+h)}, h\ne 0$

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