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Could you please share it's answer with explanation? Thanks

Could you please share it's answer with explanation? Thanks

Question Image
Grade:10

1 Answers

Aditya Gupta
2080 Points
2 years ago
note that the numerator can also be written as a^2(s – a)+b^2(s – b)+c^2(s – c), where s= a+b+c= 22
so that a^2(s – a)+b^2(s – b)+c^2(s – c) = s(a^2+b^2+c^2) – (a^3+b^3+c^3 – 3abc) – 3abc
now s^2= a^2+b^2+c^2 + 2(ab+bc+ca)
or a^2+b^2+c^2= s^2 – 2(91abc)
also we know the identity a^3+b^3+c^3 – 3abc= s(s^2 – 3(ab+bc+ca))= s^3 – 3s(91abc)
so numerator N= s(s^2 – 2(91abc)) – 3abc – s^3+3s(91abc)= – 2s(91abc) – 3abc + 3s(91abc)= abc(91s – 3)
or N/abc= 91s – 3 = 91*22 – 3= 1999

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