Show that ( b + c ) 2 3 b c + ( c +...

Michelle Mendoza

Michelle Mendoza

Answered

2022-07-10

Show that ( b + c ) 2 3 b c + ( c + a ) 2 3 a c + ( a + b ) 2 3 a b = 1
If a 3 + b 3 + c 3 = 3 a b c and a + b + c = 0 show that ( b + c ) 2 3 b c + ( c + a ) 2 3 a c + ( a + b ) 2 3 a b = 1

Answer & Explanation

SweallySnicles3

SweallySnicles3

Expert

2022-07-11Added 21 answers

a + b + c = 0 b + c = a ( b + c ) 2 = a 2
( b + c ) 2 3 b c = a 3 3 a b c
Actually, b + c = a ( b + c ) 3 = ( a ) 3
a 3 = b 3 + c 3 + 3 b c ( b + c ) = b 3 + c 3 + 3 b c ( a ) a 3 = 3 a b c
ziphumulegn

ziphumulegn

Expert

2022-07-12Added 4 answers

( b + c ) 2 3 b c + ( c + a ) 2 3 a c + ( a + b 2 ) 3 a b = a ( b + c ) 2 3 a b c + b ( c + a ) 2 3 a b c + c ( a + b 2 ) 3 a b c = a 3 3 a b c + b 3 3 a b c + c 3 3 a b c = a 3 + b 3 + c 3 3 a b c = 3 a b c 3 a b c = 1

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