(x^a / x^b)^{a^2 + ab + b^2} (x^b / x^c)^{b^2 + bc + c^2} (x^c / x^a)^{c^2 + ca + a^2} equals

Question

\(\left(\frac{x^a}{x^b}\right)^{a^2 + ab + b^2} \left(\frac{x^b}{x^c}\right)^{b^2 + bc + c^2} \left(\frac{x^c}{x^a}\right)^{c^2 + ca + a^2}\) equals

(a) a³ + b³ + c³

(b) 1

(c) (a + b + c)³

(d) 0

Answer 1

Correct option is (b) 1

\(\left(\frac{x^a}{x^b}\right)^{a^2 + ab + b^2} \left(\frac{x^b}{x^c}\right)^{b^2 + bc + c^2} \left(\frac{x^c}{x^a}\right)^{c^2 + ca + a^2}\)

\(= (x^{a−b})^{a^2+ab+b^2}×(x^{b−c})^{b^2+bc+c^2}×(x^{c−a})^{c^2+ca+a^2}\)

= 1