Prove that : (i) (xaxb)a2+ab+b2×(xbxc)b2+ab+c2×(xcxa)c2+ca+a2=1 (ii

1.	Prove that : (i) (xaxb)a2+ab+b2×(xbxc)b2+ab+c2×(xcxa)c2+ca+a2=1 (ii) (xaxb)c×(xbxc)a×(xcxa)b=1
Answer» Prove that : (i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + a b + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$ (ii) ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

Prove that : (i) (xaxb)a2+ab+b2×(xbxc)b2+ab+c2×(xcxa)c2+ca+a2=1 (ii) (xaxb)c×(xbxc)a×(xcxa)b=1

Answer»

Prove that :

(i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + a b + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$

(ii) ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

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Prove that : (i) (xaxb)a2+ab+b2×(xbxc)b2+ab+c2×(xcxa)c2+ca+a2=1 (ii) (xaxb)c×(xbxc)a×(xcxa)b=1

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