Xavier Aptitude Test 2022 Paper

Question : 53 of 100

Marks: +1, -0

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?

Validate

Solution:

Considering the two numbers to

a, b

:
We were given that :

a^3 +b^3 = 128

1/a^3 + 1/b^3 = 2

({a^3 + b^3})/({a^3 . b^3}) = 2 = 128/k

k=64

Hence,

a^3 . b^3 =64

a×b = 4

and

a^2 . b^2 =16

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