The sum of the squares of 3 natural numbers is 1029, and they are in the proportion 1 : 2 : 4. The difference between greatest number and smallest number is:
Let the smallest number be x.
Numbers are x, 2x, 4x.Â
The sum of the squares of 3 natural numbers = 1029
$$x^2 + (2x)^2 +Â (4x)^2 = 1029$$
$$x^2 +Â 4x^2 + 16x^2 = 1029$$
$$x^2 = 1029/21$$
$$x^2 = 49$$
$$x = 7$$
Smallest number = 7
Greatest number = 4x = 4 $$\times$$ 7 = 28
The difference between greatest number and smallest number = 28 - 7 = 21
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