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CBSE Class 8 Answered

a+b+c=1, a²+b²+c²=9, a³+b³+c³=1, then 1/a+1/b+1/c=?  
Asked by tavutukavitha | 30 Jun, 2020, 08:27: AM
answered-by-expert Expert Answer
Using the identity, a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2 - ab - bc - ca) + 3abc ... (i)
a plus b plus c equals 1 rightwards double arrow a squared plus b squared plus c squared plus 2 left parenthesis a b plus b c plus c a right parenthesis equals 1 rightwards double arrow 9 plus 2 left parenthesis a b plus b c plus c a right parenthesis equals 1 rightwards double arrow a b plus b c plus c a equals negative 4 U sin g space left parenthesis i right parenthesis comma space w e space h a v e 1 equals 1 left parenthesis 9 minus left parenthesis negative 4 right parenthesis right parenthesis plus 3 a b c rightwards double arrow 3 a b c equals 1 minus 13 equals negative 12 rightwards double arrow a b c equals negative 4 C o n s i d e r comma 1 over a plus 1 over b plus 1 over c equals fraction numerator a b plus b c plus c a over denominator a b c end fraction equals fraction numerator negative 4 over denominator negative 4 end fraction equals 1
Answered by Renu Varma | 01 Jul, 2020, 01:23: PM

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