Question

X= 2^1/3+2^-1/3; then find the value of 2X^3-6

Answer 1

Answer:

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If x=2+2

2/3

+2

1/3

, then the value of x

3

−6x

2

+6x is

Medium

Solution

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Correct option is B)

Given, x=2+2

2/3

+2

1/3

⇒(x−2)=2

2/3

+2

1/3

⇒(x−2)=2

2/3

+2

1/3

On cubing both sides, we get

(x−2)

3

=2

2

+2+3⋅2

2/3

⋅2

1/3

(2

2/3

+2

1/3

)

⇒x

3

−6x

2

+12x−8=4+2+3×2×(x−2)

⇒x

3

−6x

2

+6x=2.

Answer 2

Given,

X = 2^$\frac{1}{3}$ + 2^$\frac{-1}{3}$

To Find,

The value of 2X³- 6

Solution,

X = 2^$\frac{1}{3}$ + 2^$\frac{-1}{3}$

On cubing both the sides, we get

⇒ (X)³ = (2^$\frac{1}{3}$ + 2^$\frac{-1}{3}$)³

⇒ (X)³ = 2 - 2 + 3 × 2^$\frac{1}{3}$ × 2^$\frac{-1}{3}$ ( 2^$\frac{1}{3}$ + 2^$\frac{-1}{3}$)

⇒ (X)³ = 0 + 3 × 2⁰ (X)

⇒ (X)³ = 3X

⇒ X = √3

⇒ X = 1.732

∴ Substituting the value of X in the finding value,

⇒ 2X³- 6

⇒ 2 × (1.732)³ - 6

⇒ 2 × 5.189 - 6

⇒ 10.378 - 6

⇒ 4.378

Hence, the value of 2X³- 6 is 4.378