The sum of three positive numbers in an arithmetic progression is 27, and the sum of their squares is 293. Let denotes these three numbers in that order. Submit your answer as .
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a + a-d + a+d = 27 => 3a = 27 => a=27/3 = 9
and (9-d)^2 + 81 + (9+d)^2 = 293 => d = +- 5
Hence , 9 - 5 = 4 ,
Similarly, Second term = 9 and third = a + d = 9 + 5 = 14
Hence: (\lambda )^{ 2 }-(\xi )+2 \mu = (4)^2 - 14 + 2 (9) = 20