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Question
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
Solution
Given, `(1/2)^3 + (1/3)^3 - (5/6)^3` or `(1/2)^3 + (1/3)^3 + (- 5/6)^3`
Here, we see that,
`1/2 + 1/3 - 5/6`
= `(3 + 2 - 5)/6`
= `(5 - 5)/6`
= 0
∴ `(1/2)^3 + (1/3)^3 - (5/6)^3 = 3 xx 1/2 xx 1/3 xx (-5/6)` ...[Using identity, if a + b + x = 0, then a3 + b3 + c3 = 3abc]
= `- 5/12`
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