If 9x² - 6x + 1 = 0, then the value of 27x³ + (27x³)⁻¹ will be:

If 9x² - 6x + 1 = 0, then the value of 27x³ + (27x³)⁻¹…

If 9x² - 6x + 1 = 0, then the value of 27x³ + (27x³)^-1 will be:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 2.

Given:

9x² - 6x + 1 = 0 ...(i)

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Explanation:

Dividing equation (i) by 3x, we get

⇒ $3x + { 1\over 3x} = 2$

Now, taking cube of both sides, we get

⇒ ${(3x + { 1\over 3x})^3} = 2^3$

⇒ $27x^3 + {1 \over 27x^3} + 3(3x \times {1\over 3x})(3x + {1 \over 3x)} = 8$

⇒ $27x^3 + {1 \over 27x^3} + 3(2) = 8$

⇒ $27x^3 + {1 \over 27x^3} = 8 -6$

⇒ $27x^3 + {1 \over 27x^3} = 2$

Hence the required answer is 2.