Question

The sum of the square of the three consecutive even natural numbers is $1460$. Find the numbers?

• A. $18,20,22$
• B. $20,22,24$
• C. $22,24,26$
• D. $24,26,28$

Answer 1

The correct option is B $20,22,24$

Let three consecutive even natural numbers are $2n,2n+2,2n+4.$

where, $n\in .N$

Given that:

Sum of square of the three consecutive even numbers $=1460$

Now, $(2n{)}^2+(2n+2{)}^2+(2n+4{)}^2=1460$

$\Rightarrow 4n^2+4n^2+8n+4+4n^2+16n+16=1460$

$\Rightarrow 12n^2+24n-1440=0$

$\Rightarrow n^2+2n-120=0$

$\Rightarrow (n+12)(n-10)=0$

$\Rightarrow n=-12$ or, $n=10$

$n$ can't be negative.

So, $n=10$

So, three consecutive even natural numbers are $20,22,24.$

Hence, B is the correct option.