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

Question

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 · Accepted Answer

Correct Answer: 576

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

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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: 576Option 2: 250Option 3: 640Option 4: 512

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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