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The sum of three numbers in AP is 12 and sum of their cubes is 288.Find the numbers.

Posted by Akash Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let the three numbers in A.P. be {tex}a - d, a, a + d{/tex}.
{tex}3a = 12 {/tex}or, {tex}a = 4{/tex}.
Also, (4 - d)³ + 4³ + (4 + d)³ = 288
or, 64 - 48d + 12d²- d³ + 64 + 64 + 48d + 12d² + d³ = 288
or, 24d² + 192 = 288
or, 24d²= 288 - 192
or, 24d² = 96
or, d² = 96/24
or, d² = 4
d ={tex}\pm{/tex}2
The numbers are 2,4, 6, or 6,4,2.

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