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Question
Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.
Solution
Let the numbers be 2x, 3x and 4x, respectively.
∵ Sum of their cubes = 0.334125 ...[Given]
According to the question,
(2x)3 + (3x)3 + (4x)3 = 0.334125
⇒ 8x3 + 27x3 + 64x3 = 0.334125
⇒ 99x3 = 0.334125
⇒ x3 = `0.334125/99`
⇒ x3 = 0.003375
⇒ x3 = `3375/1000000`
⇒ x = `root(3)((15 xx 15 xx 15)/(10 xx 10 xx 10 xx 10 xx 10 xx 10)` ...[Taking cube root on both sides]
⇒ x = `15/(10 xx 10)`
∴ x = 0.15
Hence, the required numbers are 2 × 0.15, 3 × 0.15 and 4 × 0.15 i.e. 0.3, 0.45 and 0.6.
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