Question : The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the product of the two given numbers?
Option 1: 160
Option 2: 320
Option 3: 240
Option 4: 200

Question

Question : The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the product of the two given numbers?

Option 1: 160

Option 2: 320

Option 3: 240

Option 4: 200

Team Careers360 · Accepted Answer

Correct Answer: 240

Solution : Let the two numbers be $a$ and $b$,
According to the question,
$a + b = 32$
and, $a^{3}$ + $b^{3} = 9728$
Now,
$(a+b)^{3} = a^{3}+b^{3}+3ab(a+b)$
⇒ $32^{3} = 9728$ + $3ab(32)$
⇒ $ab=\frac{32768 − 9728}{96}$
$ herefore$ $ab = 240$
Hence, the correct answer is 240.

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Question : The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the product of the two given numbers?Option 1: 160Option 2: 320Option 3: 240Option 4: 200

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Question : The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the product of the two given numbers?
Option 1: 160
Option 2: 320
Option 3: 240
Option 4: 200