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Q-There are four positive consecutive even numbers and three positive consecutive odd numbers. the smallest odd number is 7 less than the greatest Even Numbers. the average of the square of the four consecutive even number is 29 less than the sum of the squares of the three consecutive odd numbers. find the greatest even number ? 1)8 2)10 3)12 4)14
Answers
Answer:
the answer is option 2). 10
Greatest Even number = 10
Step-by-step explanation:
Let say greatest Even number = n
Then other even numbers
n-2 , n - 4 , n - 6
4 Consecutive even numbers
n-6 , n - 4 , n - 2 , n
the smallest odd number is 7 less than the greatest Even
=> n - 7 is smallest odd number
n-7 , n - 5 , n - 3 are the consecutive odd numbers
average of the square of the four consecutive even number
=( (n-6)² + (n-4)² + (n - 2)² + n²)/4
= ( n² + 36 - 12n + n² + 16 - 8n + n² + 4 - 4n + n²)/4
= (4n² + 56 - 24n)/4
= n² - 6n + 14
sum of the squares of the three consecutive odd numbers
= (n - 7)² + (n - 5)² + (n - 3)²
= n² + 49 - 14n + n² + 25 - 10n + n² +9 - 6n
= 3n² - 30n + 83
n² - 6n + 14 = 3n² - 30n + 83 - 29
=> 2n² - 24n + 40= 0
=> n² - 12n + 20 = 0
=> n² - 2n - 10n + 20 = 0
=> n(n - 2) - 10(n - 2) = 0
=> (n - 10)(n - 2) = 0
=> n = 10
as n = 2 will lead into -ve integers for
Greatest Even number = 10
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