Question

Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.

Answer 1

Let numbers be x-1,x,x+1,x+2,x+3

(x-1)^2 + x^2 + (x+1)^2 = (x+2)^2 + (x+3)^2

$( x^{2} -2*x+1)+ x^{2} +( x^{2} +2*x+1)= ( x^{2} +4x+4)+( x^{2} +6x+9)$
$3 x^{2} +2=2 x^{2} +10x+13⇒ x^{2} =10x+11⇒ x^{2} -10x-11=0$

x=11 or -1(not a whole number)
x=11
the numbers are 10,11,12,13,14