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JATIN JAIN

· started a discussion

· 1 Months ago

jatin (Question: 187209.0 )

how a+b+c=0

Question:
If u, v, w are real numbers such that u3 – 8v3 – 27w3 = 18uvw, which one of the following is correct?
Options:
A) u – v + w = 0
B) u = –v = –w
C) u – 2v = 3w
D) u + 2v = – 3w
Solution:

Ans: (C) u3 – 8v3 – 27w3 = 18 uvw

(u)3 + (–2v)3 + (–3w)3 – 3 × (u)(–2v)(–3w) = 0

a3 +b3 +c3 – 3abc = 0

So, a + b + c = 0

u – 2v – 3w = 0

u – 2v = 3w

Knowledge Expert

· commented

· 1 Months ago

its formula:

If a + b + c = 0
∴ a + b = - c
∴ ( a + b )³ = (-c)³
∴ a³ + b³ + 3ab(a+b) = - c³
∴ a³ + b³ + 3ab( - c ) = - c³
∴ a³ + b³ + c³ = 3abc
∴ ( a³ + b³ + c³ ) ÷ ( abc ) = 3
∴ ( a³ + b³ + c³ ) = 3abc
∴ ( a³ + b³ + c³ ) - 3abc =0
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