help please I tried 4 times
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a, b, c are in continued proportion
=> a/b = b/c => b² = ac
So
( a + b + c ) ( a - b + c )
= ( a + c )² - b²
= a² + 2ac + c² - ac
= a² + ac + c²
= a² + b² + c²
=> ( a² + b² + c² ) / ( a + b + c ) = a - b + c
Now a² + b² + c² = 133 and a + b + c = 19
=> a - b + c = 133 / 19 = 7
Thus
2b = ( a + b + c ) - ( a - b + c ) = 19 - 7 = 12 => b = 6
This leaves a + c = 19 - 6 = 13 and a² + c² = 133 - 6² = 97.
Taking a = 4 and c = 9 finishes this off.
So a = 4, b = 6, c = 9 have sum 19 and sum of squares 133.
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