Question

the sum of 3 numbers in ap is 12 and the sum their cubes is 288 . find the numbers

Answer 1

Hey ❗

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↪Let the numbers be a , a+ d , a-d

↪a + a - d + a + d = 12

↪3a = 12

↪a = 4

↪According to the question !!

↪a ^3 + (a + d) ^3 + (a - d)^3 = 288

↪Now using the identies and by putting the values of a we will get

↪24 d^2 = 288 - 192

↪24 d^2 = 96

↪d^2 = 96 / 24

↪d^2 = 4

↪d = √4

↪d = +2

↪Hence for d = +2

↪a = 4 - d

↪a = 4 +2

↪a = 2

↪For d = -2

↪a = 4 - d

↪a = 4 - (-2)

↪a = 4 + 2

↪a = 6

↪So the numbers are 6 , 4 & 2

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