Question

If a=2^1/3+2^2/3 , Then prove that a^3-6a+6=0

Answer 1

Answer:

a = 2^1/3 - 2^(-1/3)

a + 2^(-1/3)= 2^1/3…………………(1(

On cubing both sides

a^3 +3.a.2^(-1/3)(a+2^(-1/3)+ 2^-1 =2

putting {a+ 2^(-1/3)}=2^1/3 from eq (1).

a^3+3.a.2^(-1/3)(2^1/3) +1/2= 2

or 2a^3+6a +1 =4

or 2a^3+6a - 3 = 0 , Answer.

Answer 2

Answer ;

Given

a=2^1/3+2^2/3

=2^1/3+2/3. ( a^m +a^n = a^m+n )

=2^3/3

=2

then

a^3-6a+6= 2^3-6(2)+6

= 8-12+6

=14-12

=2