A (relatively) Simple Radical Equation: 4p^{1/2} + 5p = 0
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Steven G
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You really should be able to handle \(\displaystyle 1-\frac{1}{2}\) and know that \(\displaystyle \frac{1}{2}<1\)
4p1/2+5p = p1/2(4+ 5p1/2)=0
So either p1/2=0 or (4+ 5p1/2)=0
Continue....
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Dr.Peterson
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Do you see what tkhunny is hinting at? You can do a substitution, letting [MATH]z = p^{1/2}[/MATH].
Of course, in a sense you will still be factoring out [MATH]p^{1/2}[/MATH], but it will be called [MATH]z[/MATH] while you are doing it!
Another way is to isolate [MATH]p^{1/2}[/MATH], which is [MATH]\sqrt{p}[/MATH], and then square both sides. This is a standard way to solve radical equations. I don't think this is the best way, though.
But it might be a good idea to look at the equation a little first. Notice that [MATH]4p^{1/2}[/MATH] is non-negative. Does that imply anything about p?
Steven G
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Ouch, I did not see that-until I factored. Thanks!
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