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How do I decide if it’s a real solutions or extraneous solutions?

How do I decide if it’s a real solutions or extraneous solutions?-example-1

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Explanation:

So you can check for extraneous solutions by plugging in the 5 and -2 as x.

Plug 5 in as x


5=√(3(5)+10)\\5=√(15+10)\\5=√(25)\\5=5

I'm not sure if this is exactly considered an extraneous solution, but I'm assuming it is, since technically the radical doesn't have a plus/minus in front of it, so it's the principle square root which means it only outputs the positive values. This would mean that the -2 wouldn't be a solution, since the principle square root doesn't output negative values, so it's a function, since if it outputted 2 values, then it wouldn't be a function by definition.

User Viktor K
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