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a+b+c=12 ,a^2+b^2+c^2=90 find a^3+b^3+c^3-3abc

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a+b+c=12 ,a^2+b^2+c^2=90 find a^3+b^3+c^3-3abc

Posted by Pranav Kaul 8 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Amar Kumar 8 years, 5 months ago

a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)

a³+b³+c³-3abc=(12)(90-(ab+bc+ca)) eq.(1)

(a+b+c)² =a²+b²+c²+2ab+2bc+2ca

2ab+2bc+2ca=(a+b+c)² -(a²+b²+c²)

2(ab+bc+ca)=12²-90

2(ab+bc+ca)=144-90

ab+bc+ca=27 eq.(2)

put value of (2) in (1)

a³+b³+c³-3abc=12(90-27)

a³+b³+c³-3abc=756

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CBSE > Class 09 > Mathematics