D/fa+b+c#0then prove that(b+c)2+_+ (a+b)2-1.c+a3ca3ab

1.	D/fa+b+c#0then prove that(b+c)2+_+ (a+b)2-1.c+a3ca3ab
Answer» HIT THE LIKE BUTTON IF YOU ARE SATISFIED (b+c)²/3bc+(c+a)²/3ac+(a+b)²/3ab =(b²+2bc+c²)/3bc+(c²+2ac+a²)/3ac+(a²+2ab+b²)/3ab =(ab²+2abc+ac²+bc²+2abc+a²b+a²c+2abc+b²c)/3abc ={ab(a+b)+bc(b+c)+ac(a+c)+6abc}/3abc=(-abc-abc-abc+6abc)/3abc [∵, a+b+c=0,∴,a+b=-c,b+c=-a,a+c=-b] =(6abc-3abc)/3abc=3abc/3abc=1 (Proved)

Answer»

HIT THE LIKE BUTTON IF YOU ARE SATISFIED

(b+c)²/3bc+(c+a)²/3ac+(a+b)²/3ab

=(b²+2bc+c²)/3bc+(c²+2ac+a²)/3ac+(a²+2ab+b²)/3ab

=(ab²+2abc+ac²+bc²+2abc+a²b+a²c+2abc+b²c)/3abc

={ab(a+b)+bc(b+c)+ac(a+c)+6abc}/3abc=(-abc-abc-abc+6abc)/3abc [∵, a+b+c=0,∴,a+b=-c,b+c=-a,a+c=-b]

=(6abc-3abc)/3abc=3abc/3abc=1 (Proved)

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