Question

The sum of square of two consecutive natural numbers is 244. Find the numbers

Answer 1

Heya..!!!

Let the no. be x , (x + 2)

x² + (x + 2)² = 244

=> X² + x² + 4 + 4x = 244

=> 2x² + 4x - 240= 0

=> X² + 2x - 120 = 0

=> X² + 12x - 10x - 120 = 0

=> X(x + 12) - 10(x + 12) = 0

=> (X - 10)(x + 12)

=> X = 10 , -12

Non be 10 , (10 + 2) = 12

Answer 2

The sum of the squares of two consecutive integers is 244. Find the two integers.
Sol'n:think it two consecutive even integers, not a consecutive integers
let x-the first number
x+1-the second number
x^2+(x+2)^2 = 244
x^2+x^2+4x+4 = 244
2x^2+4x+4 = 244
2x^2+4x-240=0
by quadratic formula:
x=10 & -12
then,
if x = 10,x+2 = 12 ---answer
and
if x = -12, x+2 = -10 ----answer