Question

if x=2-2^2/3-2^1/3 find the value of x^3-6x^2+6x+10​ please answer it I will mark it as brainliest I need correct answer

Answer 1

Answer: 0

Step-by-step explanation:

x = 2 - 2^2/3 - 2^1/3

x - 2 = - (2^2/3 + 2^1/3) ###remember

Cube on both sides

(x - 2)^3 = - (2^2/3+2^1/3)^3

L.H.S:

Use formula (a-b)^3 = a^3 - 3ab(a-b) - b^3.

(x - 2)^3 = x^3 - 6x^2 + 12x - 8.

R.H.S:

Use formula (a+b)^3 = a^3 + 3ab(a+b) + b^3

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

- [(2^2/3)^3 + 3*2^2/3*2^1/3(2^2/3 + 2^1/3) + (2^1/3)^3]

Replace 2^2/3 + 2^1/3 with -(x-2) marked as ####remember previously

Also use formula a^m * a^n = a^m+n

- [2^2 + 3*2^1[-(x-2)] + 2^1]

- [6 + 6(2-x)]

6x - 18.

L.H.S = R.H.S

x^3-6x^2+12x-8 = 6x-18

x^3 - 6x^2+(12x-6x) +(-8+18) = 0

x^3 - 6x^2+6x+10 = 0