Question

Find three numbers in A.P.such that their sum is 24 and the sum of their square is 200?

Answer 1

a + (a+d) + (a+2d) = 27
a^2 + (a+d)^2 + (a+2d)^2 = 341
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3a + 3d = 27
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a + d = 9
a^2 + 9^2 + (9+d)^2 = 341
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a + d = 9
a^2 + 9^2 + 9^2 + 18d + d^2 = 341
a^2 +18d + 162 + d^2 = 341
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a + d = 9
a^2 + 18d + d^2 = 179
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a = 9-d
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(9-d)^2 + 18d + d^2 = 179
81-18d+d^2 + 18d + d^2 = 179
81 + 2d^2 = 179
2d^2 = 98
d^2 = 49
d = 7
Then a = 2