sq.root(a^-1 b) x sq.root(b^-1c ) x sq.root(c^-1 a) = ?

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Solution

$\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a} = \sqrt{\frac{b}{a}} \times \sqrt{\frac{c}{b}} \times \sqrt{\frac{a}{c}} = 1$

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Prove that:

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

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\frac{1}{1 + x^{(b - a)} + x^{(c - a)}} + \frac{1}{1 + x^{(a - b)} + x^{(c - b)}} + \frac{1}{1 + x^{(b - c)} + x^{(a - c)}} = ?

x : \frac{1}{a + b + x} = \frac{1}{a} + \frac{1}{b} + \frac{1}{x}, [a, b, x \neq 0, x \neq - (a + b)]

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