Question

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 ?

Answer 1

$\fontsize{18}{10}{\textup{\textbf{The greatest even number is 10.}}}$

Step-by-step explanation:

Let the four consecutive even numbers be n-2, n, n+2, n n+4 and the three consecutive odd numbers be m-2, m,m+2, where n and m are positive even and odd numbers respectively.

Then, according to the given information, we have

$(m-2)+7=n+4\\\\\Rightarrow m+5=n+4\\\\\Rightarrow m=n-1.$

So, the consecutive odd numbers becomes n-3, n-1, n+1.

Also, we have

$\dfrac{(n-2)^2+n^2+(n+2)^2+(n+4)^2}{4}+29=(n-3)^2+(n-1)^2+(n+1)^2\\\\\\\Rightarrow \dfrac{4n^2+8n+24}{4}+29=3n^2-6n+11\\\\\Rightarrow n^2+2n+35=3n^2-6n+11\\\\\Rightarrow 2n^2-8n-24=0\\\\\Rightarrow n^2-4n-12=0\\\\\Rightarrow n^2-6n+2n-12=0\\\\\Rightarrow (n-6)(n+2)=0\\\\\Rightarrow n=6,-2.$

Since n is a positive even number, so n = 6.

Therefore, the greatest even number is n + 4 = 6 + 4 = 10.

Thus, the greatest even number is 10.

Learn more#

Question : The sum of three consecutive odd integers is 21 less than 4 times the largest number. Find the 3 numbers.

Link : https://brainly.com/question/13592873.