The sum of squares of two consecutive even natural number is 244. Find the numbers.

Answer

The required consecutive even natural numbers are 10 and 12.

Explanation

Let the two consecutive even natural numbers be x and x+2.
Then `x^(2)+(x+2)^(2)=244`
`:.x^(2)+x^(2)+4x+4-244=0`
`:.2x^(2)+4x-240=0`
`:.x^(2)+2x-120=0" "……` (Dividing by 2)
`:.x^(2)+12x-10-120=0`
`:.x(x+12)-10(x+12)=0`
`:.(x+12)(x-10)=0`
`:.x+12=0orx-10=0`
`:.x=-12orx=10`
But -12 is not a natural number.
`:.x=-2` is unacceptable. x=10 and x+2=10+2=12