Stupid question (1 Viewer)

[Rorix]

-2 = (-2)^1 =/= ((-2)^2)^1/2

this is the wonder of mathematics:
(x^2)^(1/2) =/= x

but (x^2)^(1/2) = |x|

sqrt4 = 2.

 

[Rorix]

stop stealing my thunder

 

[CrashOveride]

sqrt4 = 2.

The principal square root of 4 is 2, the other sqaure root is -2 ^.^

 

[Constip8edSkunk]

sqrt4 = 2

however, it is often asked in the form: find x such that x² = 4,
then |x| = 2 after taking sqrt on both sides, so x = +/-2

 

[coca cola]

sqrt4 = 2

however, it is often asked in the form: find x such that x² = 4,
then |x| = 2 after taking sqrt on both sides, so x = +/-2

This symbol, the radical:

is defined to be positive or principal root

It is often intepreted as square root on paper because people can't be bothered to put + or - in front of it. Hence the confusion.

|x| = principal or positive root of (x^2). Not square root. Square root is always defined for both positive and negative.

 

[shazzam]

hey I've looked at q5 1996, but I don't see why you would need to do anything that you've mentioned. In these papers I have here you're trying to prove that c is even, in which case you'd use sum/products of roots then subsitution.

for your q. For any real no, if your put it to the power of 1^3 ie take the cube root, then the result is always the same sign as what you began with, because it is an odd root. So initially you had x^4, and this is positive, thus x^4/3 is also positive.

 

[Danny11]

hey I've looked at q5 1996, but I don't see why you would need to do anything that you've mentioned. In these papers I have here you're trying to prove that c is even, in which case you'd use sum/products of roots then subsitution.

how do you use sum/products for that question? there is not enough information given for that to work.

 

[shazzam]

If you and I are speaking of the same q, ie 1996 q5 pt b has four miniparts, Question begins with Consider the polynomial eq....

then pt vi, you know all the roots other than alpha, say, as it's given and proved. roots namely 2, ki, -ki. Then you find alpha then work with your sums/products...

alternatively you could work from the previous part ie find P92) knowing c^2+a^2d=abc...

hmm yes i still don't know how this relates to x^4/3 being positive though...

 

[Danny11]

oh i see. that takes long though, i was thinking the other method.

 

[shazzam]

hmm which one is that?