## yociyoci 2 years ago Can someone guide me through inequality questions? i) 15-2y-y^2<0 ii) 20x-4x^2-25>0

1. Mertsj

\[y^2+2y-15>0\]

2. yociyoci

so now, (y-3)(y+5)>0? and y>-5 or y<3?

3. Mertsj

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.

4. Mertsj

|dw:1361936550944:dw|

5. Mertsj

So we see that the solution is y <-5 or y>3

6. yociyoci

oh, alright. What about the second question? I got suck at (2x-3)^2 > 0

7. Mertsj

\[4x^2-20x+25<0\] \[(2x-5)(2x-5)<0\]

8. yociyoci

opps, I was looking at a different one. Yes, I got to (2x-5)^2<0

9. Mertsj

|dw:1361936871505:dw|

10. Mertsj

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

11. yociyoci

So there will be no solution in this case, but what if it is (2x-5)^2 > 0? Will this work?

12. Mertsj

Yes. Then it would be all real numbers except 0

13. yociyoci

Alright! Thank you so much!