Question

the sum of three number in AP is12 and sum of cubes is288.find the number​

Answer 1

$\huge\frak{\underline{\underline{Question:}}}$

◾️the sum of three number in AP is12 and sum of cubes is288.find the number

$\huge\frak{\underline{\underline{Answer:}}}$

Let the numbers be a-d, a, a+d

By the given conditions,

$\implies$ (a-d)+(a)+(a+d) = 12

$\implies$3a = 12

$\implies$a = 4

$\implies$(a-d)³ + a³ + (a+d)³ = 288

$\implies$a³-d³-3a²d+3ad²+a³+a³+d³+3a²d+3ad² = 288

$\implies$3a³+6ad² = 288

$\implies$a³+2ad² = 96

$\implies$4³+2(4)d² = 96

$\implies$64+8d² = 96

$\implies$8d² = 32

$\implies$d² = 4

$\implies$d = ±2

Hence the numbers are 2, 4, 6 (Using d = 2)

                                          6, 4, 2 (Using d = -2)

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