If x= 41/3+4-1/3 prove that 4x3-12x is given by a)12 b)13 c)15 d)17 - Maths -

Question

If x= 41/3+4-1/3 prove that
4x3-12x is given by
a)12
b)13
c)15
d)17

A K Daya Sir · Accepted Answer

use whole cube identity (a + b)3 = a3 +
b3 + 3ab(a + b)
-
4x3 - 12x = 4 [41/3 + 4-1/3
]3 - 12x
= 4 [43/3 + 4-3/3 +
3(41/3)(4-1/3) (41/3 +
4-1/3 )] - 12x
= 4[4 + 4-1 + 3x] - 12x
= 16 + 1 + 12x - 12x
= 17