Question

The sum of the squares of three consecutive even integers is 200. Find the integers.​

Answer 1

Let there consecutive even integers be X, x+2,x+4

X^2+(x+2)^2+(x+4)^2=200

X^2+x^2+4x+4+x^2+8x+16=200

3x^2+12x-180=0

X^2+4x+60=0

X=-10 or 6

So numbers are 6,8,10 or -10,-8,-6

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Answer 2

❍ Let the smallest even integers be x, then the other two consecutive even integers are x + 2 and x + 4.

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• ★ According to given, x² + (x + 2)² + (x + 4)² = 200.

➛ x² + (x² + 4x + 4) + (x² + 8x + 16) = 200

➛ 3x² + 12x + 20 - 200 = 0

➛ 3x² + 12x - 180 = 0

➛ x² + 4x - 60 = 0

➛ (x - 6) (x + 10) = 0

➛ x - 6 = 0 or x + 10 = 0

➛ x = 6 or x = -10

When,

• x = 6, x + 2 = 8 and x + 4 = 10;

Then,

• x = -10, x + 2 = -8 and x + 4 = -6

✿ Therefore,

• Hence, the required integers are 6, 8, 10 or -10, -8, -6.

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