Question

sum of cube of three consecutive number is 5256 find the number​

Answer 1

Step-by-step explanation:

Question :

Sum of cube of three consecutive number is 5256. Find the number.

Solution :

Let's assume the unknown consecutive numbers be (x - 1), x, (x + 1)

Sum of cubes = 5256

${\bold{\rm{⟼ \: \: \: (x \: - \: 1)³ \: + \: (x)³ \: + \: (x \: + \: 1)³ \: = \: 5256}}}$

${\bold{\rm{⟼ \: \: \: x³ \: - \: 1 \: - \: 3(x)(1)(x \: - \: 1) \: + \: x³ \: + \: x³ \: + \: 1 \: + \: 3(x)(1)(x \: + \: 1) \: = \: 5256}}}$

${\bold{\rm{⟼ \: \: \: 3x³ \: - \: 1 \: - \: 3x² \: + \: 3x \: + \: 1 \: + \: 3x² \: + \: 3x \: = \: 5256}}}$

${\bold{\rm{⟼ \: \: \: 3x³ \: + \: 6x \: = \: 5256}}}$

${\bold{\rm{⟼ \: \: \: x³ \: + \: 2x \: = \: 1752}}}$

Using hit and trial,

${\bold{⟼ \: \: \: \: \: }}{\large{\bf{\orange{x \: = \: 12}}}}$

${\bold{⟼ \: \: \: \: \: }}{\large{\bf{\orange{(x \: + \: 1) \: = \: 13}}}}$

${\bold{⟼ \: \: \: \: \: }}{\large{\bf{\orange{(x \: - \: 1) \: = \: 11}}}}$

Hence, the numbers are 11, 12, 13