Find two positive consecutive multiples of 3 such that the sum of their square is 369. The two consecutive multiples of 3 are

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Answer 1

If the first multiple of 3 is 3x

The next consecutive multiple of 3 is 3x + 3

 

(3x)² + (3x+3)² = 369

9x² + 9x² + 18x + 9 = 369

18x² + 18x - 360 = 0

18(x²+x-20) = 0

x²+x-20=0

(x+5)(x-4) = 0

x = -5 or 4

 

Since we are dealing with positive numbers

discard the -5... x=4

 

3x = 12

3x+3 = 15

 

12² + 15² = 144 + 225 = 369

 

Your numbers are 12 and 15