Question

Three numbers are in ratio 6;8:9 sum of cubes is 11656 find smallest number

Answer 1

Answer: 12

Step-by-step explanation:

Since the numbers are in the ratio, we can write the numbers as 6m, 8m, and 9m

Given, the sum of cubes is 11656

so (6m)³+(8m)³+(9m)³=11656

216m³+512m³+729m³=11656

1457m³=11656

m³=8

So m=2

So the numbers are 12, 16 and 18

Answer 2

 

Let the numbers be 6x, 8x and 9x.

a = 6x ; b = 8x ; c = 9x

⇒ a³ + b³ + c³ = 11656

⇒ (6x)³ + (8x)³ + (9x)³ = 11656

⇒ 216x³ + 512x³ + 729x³ = 11656

⇒ 1457x³ = 11656

⇒ x³ = 8

⇒ x = 2

⇒ 6x = 12

So the smallest number is "12".

   

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