15 is divided in three parts which are in arithmetic progression (A.P.) in such a way that the sum of their square is 83. Find the smallest part?
Let the three numbers be (a - d), a, (a + d) a - d + a + a + d = 15 3a = 15 a = 5 (5 - d)² + 5² + (5 + d)² = 83 25 + d² - 10d + 25 + 25 + d² + 10d = 83 2d² = 8 d² = 4 d = ± 2 series = 3,5,7
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