Question

The sum of the squares of two consecutive even natural numbers in 724. Find
the numbers.​

Answer 1

18 square plus 20 square

324+400

= exactly 724

so the answer is

sum of the squares of 18 and 20 gives 724

18 and 20

brainliest?

Answer 2

Given,

Sum of squares of two consecutive even natural numbers = 724

To find,

The two  even consecutive numbers.

Solution,

Now natural numbers are the positive integers from 1 to infinity.

Let the natural number be a and its consecutive even number will be a+2.

So, given $a^{2} + (a+2)^{2} = 724$

Simplify ,

$a^{2} + a^{2} + 4a +4 = 724$

$2a^{2}+4a-720$ = 0

$a^{2} +2a - 360 = 0$

$a = 18 ; a = -20$

Since natural numbers is to be considered.

a = 18

and consecutive even integer = 18+2 = 18+2 = 20

Hence , the two consecutive even natural numbers are 18 and 20.