Question

(a-b/a^3 - b^3)^-1 +(b - c/b^3 -^3) +(c - a/ c^3 - a^3)^-1= 2(a^2 + b^2 +c^2) + ( ab + bc + ca) prove this
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Answer 1

Step-by-step explanation:

Solving LHS

(a-b/a^3-b^3)^-1+(b-c/b^3-c^3)^-1+(c-a/c^3-a^3)^-1

={(a-b/(a-b)(a^2+ab+b^2)}^-1+{(b-c)/(b-c)(b^2+bc+c^2)}^-1+{(c-a)/(c-a)(c^2+ca+a^2)}^-1

=1/(a^2+ab+b^2)^-1+1/(b^2+bc+c^2)^-1+1/(c^2+ca+a^2)^-1

=(a^2+ab+b^2)+(b^2+bc+c^2)+(c^2+ca+a^2)

=2a^2+2b^2+2c^2+(ab+bc+ca)

=2(a^2+b^2+c^2)+(ab+bc+ca)=RHS

LHS=RHS

Hence, proved.