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D.RAJ

· started a discussion

· 1 Months ago

kindly elaborate on the explanation (Question: 188659.0 )

kindly elaborate on the explanation

Question:

If x = a (b – c), y = b (c – a) and z = c (a – b), then  \(\left ( \cfrac {x}{a} \right )^3 + \left ( \cfrac {y}{b} \right )^3 + \left ( \cfrac {z}{c} \right )^3\)  = 

Options:
A)
B)
C)
D)
Solution:
Ans: (c)


Knowledge Expert

· commented

· 1 Months ago

x = a (b – c)

x/a = (b-c)_________(1)

y = b (c – a)

y/b=(c-a)__________(2)

z = c (a – b)

z/c=(a-b)___________(3)

Add (1),(2) and (3),

x/a + y/b + z/c = 0

Since, α^3+β^3+¥^3-3αβ¥=0 if α+β+¥=0

Take α=x/a, β=y/b and ¥=z/c

Now, simply put the value of α,β and ¥ in the given equation:

α^3+β^3+¥^3=3αβ¥
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