Prove (or disprove): If \(a,b,c,d\) are positive real numbers with \(a\times b = c\times d\), then the solutions for \(x\) in the equation \( \frac {a^x+b^x}{c^x+d^x} = \frac{a+b}{c+d} \) is only \(\pm 1\).

@Krishna Sharma
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Note that he already mentioned that \(a,b,c,d\) are positive reals, so you don't need to consider non-negative reals.
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Prasun Biswas
·
1 year, 6 months ago

## Comments

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TopNewest\(a=b=c=d=1\) gives \(1 = 1\) that means the \(x\) has infinitely many solutions! – Samuraiwarm Tsunayoshi · 1 year, 6 months ago

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– Pi Han Goh · 1 year, 6 months ago

Oh. You found a loophole. Let me fix that.Log in to reply

– Prasun Biswas · 1 year, 6 months ago

I think you should make \(a,b,c,d\) distinct.Log in to reply

– Krishna Sharma · 1 year, 6 months ago

\(a = b = c = d \neq 0\) also satifies the condition.Log in to reply

positivereals, so you don't need to consider non-negative reals. – Prasun Biswas · 1 year, 6 months agoLog in to reply