# Tag Info

### Why do we sometimes lose solutions when solving equations?

One frequent cause of losing solutions is dividing by something that could be $0$. For example, you get an equation of the form $$a b = b c$$ and you jump to the conclusion $a = c$ without taking ...
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### Why do we sometimes lose solutions when solving equations?

If that is the case why do we sometimes lose solutions when solving equations? We don't. If we take an equation and perform valid operations on it, we will never lose any solutions. If we look back ...
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Accepted

### Erroneous application of AM-GM inequality.

Equality for this expression (and hence maximum for the geometric mean) is attained when $a=b=c$. This is where the error lies. For example, pick any three positive numbers $a'\ge b'\ge c'$ that are ...
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### Knowing $x^2-x-1$ is a factor of $p(x)=ax^5 + bx^4 + 1$ , find a,b.
Your method is on-target. You just need to reduce the quintic until both the equations are of same degree to compare coefficients. I will show an example with highest degree of $2$ (reduction to ...