Question

If x=21/3+22/3+2 than prove that x3-6x2+6x ?

Answer 1

Your question is incomplete.
Prove that `x^3-6x^2+6x`? ... what do you want to prove?

I have simplified so far but I cannot give you an answer with the limited information I have.

Explanation:

So far:

Assuming you meant the prove part to be `x^3-6x^2+6x`,

`x=21/3+22/3+2`,
simplify to `\color(red)(x=)43/3+2=43/3+6/3=\color(red)(49/3)`
then replace the prove equation variable.

`(\color(red)(49/3))^3-6(\color(red)(49/3))^2+6(\color(red)(49/3))`
`\rArr(117649)/(27)-6((2401)/(9))+6(49/3)`

Finding common denominator which is `9xx3xx1=27`,
`117649/27(1/1)-6(2401/9)(3/3)+6(49/3)(9/9)`
`\rArr117649/27-6(7203/27)+6(294/27)`
`\rArr117649/27-43218/27+1764/27=(117649-43218+1764)/27=76195/27`

Current progress

Answer 2

`2`.

Explanation:

I assume that the Problem is to find the value of

`x^3-6x^2+6x," given that, "x=2^(1/3)+2^(2/3)+2`.

Starting with, `x=2^(1/3)+2^(2/3)+2`, we have,

`x-2=2^(1/3)+2^(2/3)...........................(star)`.

`"Cubing, "(x-2)^3={2^(1/3)+2^(2/3)}^3`.

`:. x^3-2^3-3*x*2(x-2)`

`=(2^(1/3))^3+(2^(2/3))^3+3*2^(1/3)*2^(2/3){2^(1/3)+2^(2/3)}`.

`:. x^3-8-6x^2+12x=2+2^2+3*2(x-2)......[because, (star)]`.

`:. x^3-8-6x^2+12x=2+4+6x-12`.

`:. x^2-6x^2+12x-6x=6-12+8`.

`rArr x^3-6x^2+6x=2`, as desired!