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