If a3+b3+c3=3abc & a+b+c=0 show that (b+c)2/3bc+(c+a)2/3ac+(a+b)2/3ab=1.
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(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
a+b+c=0; so, a+b=-c..........
=(-abc-abc-abc+6abc)/3abc
=(6abc-3abc)/3abc
=3abc/3abc
=1 (Proved)
hope it helps you
=(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
a+b+c=0; so, a+b=-c..........
=(-abc-abc-abc+6abc)/3abc
=(6abc-3abc)/3abc
=3abc/3abc
=1 (Proved)
hope it helps you
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Answer:
Step-by-step explanation:
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