What is meant by a the trivial solution does away with the n

What is meant by a \"the trivial solution does away with the non trivial solution in a given interval\"?

Please explain and give an example

Trivial solution of an equation is x=y=z = 0 No, the trivial solution does not away with the non trivial solution in a given interval always, eg. x+y+z= 1 here x=y=z =0 is not a solution

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