Question

The sum of square of two consecutive even numbers is5620 find the sum of number

Answer 1

Answer:

52,54 or -52,-54

Step-by-step explanation:

Let the least number be x

So, the next consecutive number is (x+2)

Now, according to problem, x^2 + (x+2)^2 = 5620

or,  x^2 + x^2 + 4x + 4  =  5620

or,  2x^2 + 4x  =  5616

or,  2x^2 + 4x - 5616  =  0

or,  x^2 + 2x - 2808  =  0

or,  x^2 + 54x - 52x - 2808  =  0

or,  x( x + 54 ) - 52( x + 54 )  =  0

or,  ( x + 54 )( x - 52 ) = 0

either, x = -54 or, x = 52

so, the next even number may be either -52 or 54.

The numbers are 52,54 or -52,-54.

Hope this helps, please mark brainliest.

Answer 2

The sum of the numbers is 106.

Step-by-step explanation:

Let the two consecutive even numbers x and (x + 2)

To find, the sum of number = ?

According to question,

$x^2+(x+2)^2=5620$

⇒  $x^2+x^2+4x+4=5620$

⇒  $2x^2+4x = 5616$

⇒ $2x^2+4x-5616=0$

Dividing by 2, we get

⇒  $x^2+2x-2808=0$

⇒  $x^2+ 54x-52x-2808=0$

⇒  $x( x+54)-52( x+54 )=0$

⇒  $(x+54)(x-52)=0$

⇒ x = - 54 or, x = 52 [ - 54 is neglected]

∴ x = 52

⇒ x + 2 = 52 + 2 = 54

∴  The sum of number = 52 + 54 = 106

Hence, the sum of the numbers is 106.