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CBSE Class 9 Answered

If a+b+c = 12, a2 + b2 +c2 = 90, find a3 + b3 + c3 -3abc ?
Asked by nisha_vini29 | 23 Mar, 2017, 05:41: PM
answered-by-expert Expert Answer

begin mathsize 16px style straight a plus straight b plus straight c space equals 12 comma space straight a squared space plus space straight b squared space plus straight c squared space equals space 90 comma space find space straight a cubed space plus space straight b cubed space plus space straight c cubed space minus 3 abc Consider comma space 1 over straight a plus 1 over straight b plus 1 over straight c equals space fraction numerator ab plus bc plus ac over denominator abc end fraction open parentheses straight a plus straight b plus straight c close parentheses squared equals space straight a squared space plus space straight b squared space plus straight c squared space plus 2 left parenthesis ab plus bc plus ac right parenthesis rightwards double arrow 144 equals 90 space plus 2 left parenthesis ab plus bc plus ac right parenthesis rightwards double arrow ab plus bc plus ac equals 27 straight a cubed space plus space straight b cubed space plus space straight c cubed space minus 3 abc equals space left parenthesis straight a space plus space straight b space plus space straight c right parenthesis space left parenthesis space straight a squared space plus space straight b squared space plus straight c squared space space – space ab space – space bc space – space ca right parenthesis space equals space left parenthesis 12 right parenthesis space left parenthesis space 90 space – space 27 right parenthesis space equals 756 end style

Answered by | 23 Mar, 2017, 05:52: PM

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