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# 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 $$\pm 1$$.

t4t44

Note by Pi Han Goh
2 years, 8 months ago

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$$a=b=c=d=1$$ gives $$1 = 1$$ that means the $$x$$ has infinitely many solutions!

- 2 years, 8 months ago

Oh. You found a loophole. Let me fix that.

- 2 years, 8 months ago

I think you should make $$a,b,c,d$$ distinct.

- 2 years, 8 months ago

$$a = b = c = d \neq 0$$ also satifies the condition.

- 2 years, 8 months ago

Note that he already mentioned that $$a,b,c,d$$ are positive reals, so you don't need to consider non-negative reals.

- 2 years, 8 months ago