Question

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

of the numbers is 13, then the difference of the two ​

Answer 1

Answer:

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

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