Question 53

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 $$a^2\cdot b^2\ =\ 16$$

video

Create a FREE account and get:

  • All Quant Formulas and shortcuts PDF
  • 15 XAT previous papers with solutions PDF
  • XAT Trial Classes for FREE