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if a2 + b2 +c2 =280 and ab+bc+ca = 9 /2 find the value of ( a +b +c)3

Asked by nisha_vini29 13th September 2015, 12:44 AM
Answered by Expert
Answer:

G i v e n space t h a t space a squared plus b squared plus c squared equals 280 space a n d space a b plus b c plus c a equals 9 over 2 W e space n e e d space t o space f i n d space t h e space v a l u e space o f space open parentheses a plus b plus c close parentheses cubed. W e space k n o w space t h a t comma open parentheses a plus b plus c close parentheses cubed equals open parentheses a plus b plus c close parentheses squared cross times open parentheses a plus b plus c close parentheses space space space space space space space space space space space space space space space space space equals open parentheses a squared plus b squared plus c squared plus 2 open parentheses a b plus b c plus c a close parentheses close parentheses cross times open parentheses a plus b plus c close parentheses space space space space space space space space space space space space space space space space space equals open parentheses 280 plus 2 cross times 9 over 2 close parentheses cross times open parentheses a plus b plus c close parentheses space space space space space space space space space space space space space space space space space equals 289 cross times open parentheses a plus b plus c close parentheses open parentheses a plus b plus c close parentheses cubed equals 289 cross times open parentheses a plus b plus c close parentheses rightwards double arrow open parentheses a plus b plus c close parentheses squared equals 289 rightwards double arrow open parentheses a plus b plus c close parentheses squared equals 17 squared rightwards double arrow a plus b plus c equals 17 rightwards double arrow open parentheses a plus b plus c close parentheses cubed equals 17 cubed rightwards double arrow open parentheses a plus b plus c close parentheses cubed equals 4913

Answered by Expert 14th September 2015, 6:03 PM
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