The sum of the cubes of two numbers is 793. The sum of the

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The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference of the two numbers is

1. 7
2. 6
3. 5
4. 8

Correct Option: C

Let the numbers be a and b where a > b.
According to the question,
a³ + b³ = 793
and a + b = 13
∴ (a + b)³ = a³ + b³ + 3ab (a + b)
⇒ (13)³ = 793 + 3ab ×13
⇒ 2197 = 793 + 39ab
⇒ 39ab = 2197 – 793 = 1404

⇒ ab =	1404	= 36
	39

∴ (a + b)² = (a + b)² – 4ab
= (3)² = 4 × 36
= 169 – 144 = 25
⇒ a – b = √25 = 5