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Question
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
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Solution
Here, we see that, x – 2y – 6 = 0
∴ x3 + (–2y)3 + (–6)3 = 3x(–2y)(–6) ...[Using identity, a + b + c = 0, then a3 + b3 + c3 = 3abc]
⇒ x3 – 8y3 – 216 = 36xy ...(i)
Now, x3 – 8y3 – 36xy – 216
= x3 – 8y3 – 216 – 36xy
= 36xy – 36xy ...[From equation (i)]
= 0
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