perplexus.info :: Just Math : Ratio of Cubic Expressions

Ratio of Cubic Expressions (Posted on 2024-09-01)

Determine the value of this expression:

73³+34³
--------
73³+39³

No Solution Yet Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solution

| Comment 1 of 2

Note: 34+39=74 so this whole thing generalizes.

Factor both number by sum of cubes.

(73+34)(73^3-73*34+34^2)

(73+39)(73^3-73*39+39^2)

107(73^3-34(73-34))

112(73^3-39(73-39))

107(73^3-34*39)

112(73^3-39*34)

107

112

Posted by Jer on 2024-09-01 11:08:04

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