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The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.
What is the product of the squares of the numbers?
Considering the two numbers to a, b :
We were given that :
$$a^3+b^3\ =\ 128$$
$$\frac{1}{a^3}+\ \frac{1}{b^3}=\ 2$$
$$\frac{\left(a^3+b^3\right)}{a^3\cdot b^3}=\ 2\ =\ \frac{128}{k}$$
k = 64.
Hence $$a^3\cdot b^3\ =\ 64$$
a*b = 4 and $$a^2\cdot b^2\ =\ 16$$
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