if x=a(b-c) y=b(c-a) z=c(a-b) then x^2/yz+y^2/zx+z^2/xy=?
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Clearly x + y + z =0
So we have x³ + y³ + z³ = 3xyz
Now
x^2/yz+y^2/zx+z^2/xy
= x³ + y³ + z³ / xyz
= 3xyz / xyz
= 3
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