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Question : The sum of the cubes of two given numbers is 10234, while the sum of the two given numbers is 34. What is the positive difference between the cubes of the two given numbers?

Option 1: 3484

Option 2: 3488

Option 3: 3356

Option 4: 8602


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: 3484


Solution : $(a + b)^3= a^3+ b^3+ 3ab(a + b)$
$⇒(34)^3=10234+3ab(34)$
$⇒39304−10234 = 3ab(34)$
$⇒29070 = 102\times ab$
$⇒ab = \frac{29070}{102} = 285$
We know, $(a - b)^2= (a + b)^2 - 4ab$
$⇒(a - b)^2= 34^2 - 4 \times (285)$
$⇒(a - b)^2= 1156 -1140 = 16$
$⇒(a - b) = 4$ ........ (i)
Now $(a+b) = 34$ ........(i)
Solving both the equations (i) and (ii) we get,
$a = 19$ and $b = 15$
So, $a^3-b^3 = 19^3 - 15^3 = 3484$
Hence, the correct answer is 3484.

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