Question

Three numbers are in the ratio 1:2:3.The sum of their cubes is 98784. Find the numbers

Answer 1

1. Question⇒  Three numbers are in the ratio 1:2:3.The sum of their cubes is 98784. Find the numbers.

Step-by-step explanation:

• Since the numbers are in the ratio 1:2:3, let the numbers be x,2x and 3x.
• Given that the sum of three cube is 98784
• So  x³ + (2x)³ + (3x)³ = 98784
• ⇒ x³ + 8x³ + 27x³ = 98784
• ⇒ 36x³ = 98784
• ⇒ x³ = 98784 / 36 
• ⇒ x³ = 2274
• ⇒ x = ∛2274
• ⇒ x = 14
• 2x = 2 × 14 = 28
• 3x = 3 × 14 = 42
• So numbers are 14, 28 and 42.

Answer 2

Answer:

14,28,42

Step-by-step explanation:

Let the no's be : x , 2x, 3x

A.T.Q

x^3 + (2x)^3 +(3x)^3 =98784

= x^3 +8x^3 + 27x^3 = 98784

= 36x^3 = 98784

= x^3 = 98784/36

=x^3 = 2744

= x = ∛2744

= x = 14

Therefore, the no 's are 14, (2×14),(3×14)

=14,28,42

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