If a^3+b^3+c^3=3abc and a+b+c=0, prove that (b+c)^2/3bc+(c+a)^2/3ac+(a+b)^2/3ab=1.
Preet , 6 Years ago
Grade 9
9 grade maths> If a^3+b^3+c^3=3abc and a+b+c=0, prove th...
1 AnswersArnab
Last Activity: 6 Years ago
a + b + c = 0 (given)
or, b + c = - a
or, c + a = - b
or, a + b = -c
(b+c)²/3bc + (c+a)²/3ac + (a+b)²/3ab
= (-a)²/3bc + (-b)²/3ac + (-c)²/3ab
= (a)²/3bc + (b)²/3ac + (c)²/3ab
= a³+b³+c³/3abc
= 3abc/3abc (
a³+b³+c³ = 3abc)
= 1
hence proved.
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