Question

The sum of the square of three
consecutive
even integers is 200.find the number​

Answer 1

Answer:

The sum of the square of three con even integers is 200.So the numbers is 6, 8, 10

Answer 2

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

━━━━━━━━━━━━━━━━━

★ 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.

━━━━━━━━━━━━━━━━━