Question

2. If x= 2 - 2/3 + 22/3, then the

value of x- 6x² + 18x+ 18 is

(1) 22

(3) 40

(2) 33

(4) 45

Answer 1

Answer:

40

Step-by-step explanation:

x = 2 - 21 / 3 + 22 / 3

⇒ x – 2 = 22 / 3 - 21 / 3

On cubing both sides ,

⇒ x3 - 3x2 × 2 + 3x × 4 – 8 = ( 22 / 3 )3 - ( 21 / 3 )3 - 3 . 22 / 3 . 21 / 3( 22 / 3 - 21 / 3 )

⇒ x3 - 6x2 + 12x – 8 = = 4 – 2 – 6 (x – 2)

⇒ x3 - 6x2 + 12x – 8 = = 2 – 6x + 12

⇒ x3 - 6x2 + 18x + 18 = 2 + 12 + 8 + 18 = 40

Answer 2

Answer:

(3) 40

Step-by-step explanation:

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

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

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

So we get:-

=>x^3 - 8 - 3(2)(x)(x-2) = [2^2/3]^3 - [2^1/3]^3 -3([2^2/3])([2^1/3])([2^2/3]^3-     [2^1/3]^3

=>x^3 - 8 -6x^2 +12x = 4 - 2 -  3(2)(x-2) [Note :- x-2 = ([2^2/3] - [2^1/3] from question)

=>x^3 - 8 -6x^2 +12x =2 -  6x + 12

=>x^3 -22 -6x^2 +18x = 0

=>x^3 18 -6x^2 +18x = 22 + 18 (Adding 18 on both sides)

Therefore we have:-

x^3 - 6x^2 + 18x + 18 = 40