savvers
4sqrt(x+9)=20 can anyone help?



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geoffb
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\[4 \sqrt{(x+9)} = 20\]
Like this? At what part are you getting stuck?

savvers
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well i get x=16 but when i try to see if its true i get 20=20

savvers
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and yes like that

geoffb
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Yeah, with that 4 outside the square root, I think it's undefined.

savvers
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yeah your probably right. extraneous solution?

geoffb
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If we defined \(y\) as \(\sqrt{(x+9)}\), we would get \(4y = 20\), with \(y = 5\), and there is no way \(\sqrt{(x+9)} = 5\)

savvers
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hmmm i dont know. but when we divide 4 we get \[\sqrt{x+9}=5\]

geoffb
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\(\large{\sqrt{x} = i \sqrt{x}}\) right?

savvers
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yeah

geoffb
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Okay, can we use that somehow?

geoffb
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Oh wait... We can square both sides, right?

savvers
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hmmm yeah

savvers
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and we get x+9=25 because 5x5=25

geoffb
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Right, so you were right with 16; it is an extraneous root.

savvers
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yeah it looks like that then and thanks man

geoffb
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Hey, no problem. :)