Mathematics
If 3a + 5b + 4c = 0, show that :
27a3 + 125b3 + 64c3 = 180abc.
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Answer
By property,
If x + y + z = 0, then :
x3 + y3 + z3 = 3xyz ……..(1)
Comparing,
3a + 5b + 4c = 0 with x + y + z = 0, we get :
x = 3a, y = 5b and z = 4c.
Substituting values in equation (1), we get :
⇒ (3a)3 + (5b)3 + (4c)3 = 3 × 3a × 5b × 4c
⇒ 27a3 + 125b3 + 64c3 = 180abc.
Hence, proved that 27a3 + 125b3 + 64c3 = 180abc.
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