Question 74

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:

Solution

Let the smallest number be x.

Numbers are x, 2x, 4x.

The sum of the squares of 3 natural numbers = 1029

$$x^2 + (2x)^2 + (4x)^2 = 1029$$

$$x^2 + 4x^2 + 16x^2 = 1029$$

$$x^2 = 1029/21$$

$$x^2 = 49$$

$$x = 7$$

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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