Question

the sum of three numbers in AP is 12 and sum of their cubes is 288 find the numbers​

Answer 1

This is u r answer mark as brainlist

Answer 2

Answer:

The numbers are 2, 4 and 6.

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Step-by-step explanation:

Let a be the middle number and let d be the common difference.  (It's handy to let a be the middle number rather than the fast number because it can make some of the algebra easier by keeping the numbers small.)

The three numbers are:   a - d,  a,  a + d

Their sum is 12  =>  ( a - d ) + a + ( a + d) = 12  =>  3a = 12  =>  a = 4

So the numbers are:   4 - d,  4,  4 + d

The sum of their cubes is 288

=>  ( 4 - d )³ + 4³ + ( 4 + d )³ = 288

=>  ( 4³ - 3×4²×d + 3×4×d² - d³ ) + 4³ + ( 4³ + 3×4²×d + 3×4×d² + d³ ) = 288

=>  3×4³ + 2×3×4×d² = 288

=> 24 d² = 288 - 3×4³ = 288 - 192 = 96

=> d² = 96 / 24 = 4

=> d = ±2

If d = -2, the numbers in order are 4 - (-2), 4, 4 + (-2)

If d = 2, the numbers in order are 4 - 2, 4, 4 + 2

Either way, the numbers are 2, 4 and 6.