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Question : The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the sum of the cubes of the two given numbers.

Option 1: 576

Option 2: 250

Option 3: 640

Option 4: 512


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

Correct Answer: 576


Solution : Let the 2 numbers be $a$ and $b$.
According to the question,
$(a+b)^3 = 1728$
⇒ $a+b = 12$
Also, $a\times b = 32$
We have to find, $a^3 + b^3$
$(a+b)^3 = 1728$
⇒ $a^3 + b^3 + 3ab(a+b) = 1728$
⇒ $a^3 + b^3 = 1728 - 3ab(a+b)$
⇒ $a^3 + b^3 = 1728 - 3\times 32 \times 12$
⇒ $a^3 + b^3 = 1728-1152 = 576$
Hence, the correct answer is 576.

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