yociyoci
Can someone guide me through inequality questions?
i) 15-2y-y^2<0
ii) 20x-4x^2-25>0
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Mertsj
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\[y^2+2y-15>0\]
yociyoci
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so now, (y-3)(y+5)>0? and y>-5 or y<3?
Mertsj
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The first part is right. If you multiply two factors and get a positive result, then both factors must be positive or both factors must be negative.
Mertsj
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|dw:1361936550944:dw|
Mertsj
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So we see that the solution is y <-5 or y>3
yociyoci
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oh, alright. What about the second question? I got suck at (2x-3)^2 > 0
Mertsj
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\[4x^2-20x+25<0\]
\[(2x-5)(2x-5)<0\]
yociyoci
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opps, I was looking at a different one. Yes, I got to (2x-5)^2<0
Mertsj
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|dw:1361936871505:dw|
Mertsj
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Oh, it will never be less than 0 but of course we already knew that a real number raised to the second power will always be positive or 0 and never less than 0
yociyoci
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So there will be no solution in this case, but what if it is (2x-5)^2 > 0? Will this work?
Mertsj
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Yes. Then it would be all real numbers except 0
yociyoci
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Alright! Thank you so much!