Correct Answer: 81

Solution : Given:
x ⁶ – 18x ³ + k
Let x ³ = y
The given expression becomes y ² – 18y + k.
Now break the expression into the form of (a – b) ² = a ² – 2ab + b ²
So, y ² – 18y + k = y ² – 2(y)(9) + k
For the above expression to be a perfect square, k should be equal to (9) ² = 81
= y ² – 2(y)(9) + 9 ²
= (y – 9) ²
Substituting the value of y in the above expression, we get,
(x ³ – 9) ² , which is a perfect square.
Hence, the correct answer is 81.