Question 316952: Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same.
You can put this solution on YOUR website! Find three consecutive odd whole numbers such that the sum of their squares is a four-digit whole number whose digits are all the same
:
Three consecutive odd numbers x, (x+2), (x+4); resulting 4 number digit = y
:
x^2 + (x+2)^2 + (x+4)^2 = 1000y+100y+10y+y
:
x^2 + x^2+4x+4 + x^2+8x+16 = 1111y
:
x^2 + x^2 + x^2 + 4x + 8x + 4 + 16 = 1111y
:
3x^2 + 12x + 20 = 1111y
:
y =
:
Find the value for x which gives an integer value to y (the table of a TI83 was a great help!)
x=41, y=5
:
41^2 + 43^2 + 45^2 = 5555
