Monday, 17 February 2014

Algebra... Which is larger? (II)

Jennifer says, "5x2  is always smaller than  (-5x)2. "

This question is compulsory.

1. This comment has been removed by the author.

2. I do not agree with Jennifer as:
Let x be 1/0
5x^2=5X1/0^2
=infinity
(-5x)^2=(-25)X1/0^2
=infinity

3. No. If x=1 then 5x squared is 5 and (-5x)squared is 25 so in this case 5x squared is smaller than (-5x) squared. However for numbers larger or smaller than one 5x squared is the same as (-5x) squared e.g. x=2 5x squared = 100
(-5x) squared is still 100.

4. no. It is wrong.
Let x be 1.
Then, 1x1=1
5x1=5
While -5x1=-5
-5 square= 25
Therefore, (-5x) square is always bigger than 5x square.

5. No. If X=1 then 5Xsquare will be 25.
Thus, (-5X)square will also be 25, which means they are equal, so Jennifer is wrong

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7. She is right unless x=0
This is because
Expression 1: 5xsq
Expression 2:(-5x)square(sq)=(-5)sqx(x)sq=25xsq
Compare Ex 1 and 2, Ex 1 is smaller.

8. No.
If X were 5, 5x square would equal to 25x. (-5x) square would also equal 25x therefore Jennifer is wrong.

9. She is wrong (unless there is a third option again XD)
If X is 1 then 5xsq will be 25 while (-5x)sq is also 25 which means they are the same,thus Jennifer is wrong.

10. She is wrong. (I hope this isn't a 'third option' kind of thing.)
If x were to be 5, 5xsq would be 25 while (-5x)sq would also be 25, which shows that the answers are indeed the same. Therefore, Jennifer is wrong

11. No.
If x = 1, 5x^2=25
(-5x)^2 = -25
So, 5x^2 is not always smaller than (-5x)^2

12. yes.
if x = 1
5 x 1^2 = 20
-5^2 x 1^2= 27

13. No,they are equal,
X=10
(5x10)sq=2500
-(5x10)sq=2500

14. No. If x = 1 then both of the results would be the same, but if x is more than one, then 5x^2 would be smaller. But nonetheless, it shows that 5x^2 is not always smaller than (-5x)^2.

15. YES..

x is a variable --- it can change.

If 'x' is zero, both answers are zero and they are the same.

If 'x' is 5, 5x to the power of 2 means (5X5) X (5X5) = 625
and (-5x) to the power of 2 means (-5 X 5 ) X (-5 X 5) = 625!
So both of them are the same.
Even If 'x' is 1, 5x to the power of 2 means (5 X 1) X (5 X 1) = 25
and (-5x) to the power of 2 means (-5 X 1) X (-5 X 1) = 25
So, both of them will be the same , No matter what, even if x is zero.

1. Sorry , I do not agree.

16. No.
If x is 1, then, 1 x 1 = 1

5 x 1 = 5
-5 x 1= -5
-5 square = 25
So, (-5x) squared is always bigger than 5x squared.

17. I do not agree.
Let's take x as 10.
5x10=50
50x50=250

And...

-5x10=(-50)
-50x-50=(-100)

So,here you can see that 5x to the power of 2 is greater.

18. I don't agree
Take x as 20
5x20=100
100x100=10000

-100x-100=10000
So they are equal.

19. I do not agree, because if x = 10, then (5 x 10)^2 = 2500 and ( -5 x 10)^2 = 2500, and so they are equal.

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21. This comment has been removed by the author.

22. I do not agree.

Scenario 1

If x = 1 ,

5x^2 = 5 x 1 x 1 = 5
(-5 x x)^2 = (-5 x 1 ) x (-5 x 1 ) = 25
5x^2 is smaller.

Scenario 2

If x = 0 ,
5x^2 = 5 x 0 x 0 = 0
(-5 x x )^2 = (-5 x 0 ) x (-5 x 0 ) = 0
Both of their values are 0 thus none of them is smaller.

From the two scenarios above , we can conclude that Jennifer is wrong.