Question

Hello people, can anybody solve it ​

Answer 1

`\\ \rm\Rrightarrow \left((x^a)/(x^(-b))\right)^(a^2-ab+b^2)* \left((x^b)/(x^(-c))\right)^(b^2-bc+c^2)* \left((x^c)/(x^(-a))\right)^(c^2-ca+a^2)=1`

`\\ \rm\Rrightarrow (x^(a+b))^(a^2-ab+b^2)* (x^(b+c))^(b^2-bc+c^2)* (x^(c+a))^(c^2-ac+a^2)=1`

`\\ \rm\Rrightarrow x^((a+b)(a^2-ab+b^2))* x^((b+c)(b^2-bc+c^2))* x^((c+a)(c^2-ca+a^2))=1`

• a³+b³=(a+b)(a²-ab+b²)

`\\ \rm\Rrightarrow x^(a^3+b^3)* x^(b^3+c^3)* x^(c^3+a^3)=1`

`\\ \rm\Rrightarrow x^(a^3+b^3+b^3+c^3+c^3+a^3)=1`

`\\ \rm\Rrightarrow x^(2a^3+2b^3+2c^3)=x^0`

`\\ \rm\Rrightarrow 2(a^3+b^3+c^3)=0`

`\\ \rm\Rrightarrow a^3+b^3+c^3=0`