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:
Answer & explanation
Correct answer: option 2
The proportion of the numbers = 1 : 2 : 4
Numbers can be represented by x, 2x, 4x
Sum of squares of these numbers = x² + 4x² + 16x² = 1029(given)
21x² = 1029
x² = 49 or x = 7
Thus, the greatest number = 4 x 7 = 28
and the smallest number = 7
Their difference = 21 - 7 =21