If the difference between two numbers is 5 and the difference between their cubes is 1850, then the difference between their squares is:
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 5
Let the numbers be a and b
According to question
a - b = 5 and a³ - b³ = 1850
Now
⇒ (a - b)³ = a³ - b³ - 3ab(a - b)
⇒ 125 = 1850 - 3ab(5)
⇒ 125 - 1850 = 3ab (5)
⇒ 15ab = 1725
⇒ ab = 115
⇒ a³ - b³ = (a - b) (a² + b² + ab)
⇒ 1850 = (5) (a² + b² + 115)
⇒ a² + b² = 255 ,
Now
(a + b)2 = a² + b² + 2ab
⇒ 255 + 2 × 115
⇒ √485
Hence,
a² - b² = (a + b) (a - b)
⇒ 5 × √485
⇒ 5√485