Question

(xa/xb)^a2+ab+b2×(xb /xc)^b2 +bc+c2 ×(xc/xa) ^c2+ca+a2

Answer 1

I hope it is not wrong and helps you

Answer 2

Answer:

1

Explanation:

Given

$\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+ab+b^{2}}$

$\times</p><p>\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+bc+c^{2}}$

$\times</p><p>\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+ca+a^{2}}$

=$\left(x^{a-b}\right)^{(a^{2}+ab+b^{2})} \times$

$\left(x^{b-c}\right)^{(b^{2}+bc+c^{2})}$

$\times</p><p>\left(x^{c-a}\right)^{(c^{2}+ca+a^{2})}$

$=x^{(a-b)(a^{2}+ab+b^{2})}$

$\times</p><p>x^{(b-c)(b^{2}+bc+c^{2})}$

$\times</p><p>x^{(c-a)(c^{2}+ca+a^{2})}$

$=x^{a^{3}-b^{3}}\times x^{b^{3}-c^{3}}\times x^{c^{3}-a^{3}}$

$=x^{a^{3}-b^{3}+b^{3}-c^{3}+c^{3}-a^{3}}$

$=x^{0}$

$= 1$

Therefore,

$\left(\frac{x^{a}}{x^{b}}\right)^{a^{2}+ab+b^{2}}$ $\times</p><p>\left(\frac{x^{b}}{x^{c}}\right)^{b^{2}+bc+c^{2}} \times</p><p>\left(\frac{x^{c}}{x^{a}}\right)^{c^{2}+ca+a^{2}}$ = 1

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