Question
The sum of the squares of three natural numbers is 342.
These numbers are in the ratio of 3:5:2. Determine the difference between the largest and smallest numbers.Solution
Let the three numbers be '3x', '5x', and '2x'.ATQ;(3x) 2 + (5x) 2 + (2x) 2 = 342Or, 9x2 + 25x2 + 4x2 = 342Or, 38x2 = 342Or, x2 = (342/38)So, x = ±9Since, the given numbers are natural we will take the positive root only. So, x = 3Smallest number = 2x = 2 X 3 = 6Greatest number = 5x = 5 X 3 = 15 Required difference = 15 - 6 = 9
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