Question

Help me please :D
Design at least three different equivalent forms of x^2
Show how each one can be simplified back to x^2 in two or more steps
HELP Please!! :)

Answer 1

x*x=x^2

Answer 2

like thAT

Answer 3

one form that comes to my mind is

\(\large \sqrt{x^4}\)

Answer 4

second form

\(\large \frac{x^5}{x^3} \)

here \(x \ne 0\)

Answer 5

can't use x*x @AllTheLonelyKillers because that is only one step.. :)

Answer 6

can u think of a third form ? maybe try putting x^2 inside log or somthing..

Answer 7

what is log? @ganeshie8

Answer 8

oh i was just giving a guess i am kinda clueless here

Answer 9

forget it, think of someother rational funciton like secondone may be :)

Answer 10

Well thank you :) @AllTheLonelyKillers

Answer 11

so I just put any number with the x & solve it? @ganeshie8

Answer 12

third form :-

\(\large \frac{x^3(x-1)}{x^2-x}\)

Answer 13

if you simplify above 3 forms, you wud end up wid \(x^2\)

Answer 14

but, each has its own domain restrictions. (ur teacher wants u to think about domain restrictions)

Answer 15

what kind of domain restrictions?

Answer 16

before we get that that,
are u convinced, all above forms simplify to \(x^2\) ? :)

Answer 17

I believe you lol b/c I have no clue how to do any of that

Answer 18

it is good if u r able to simplify them and see that they indeed give u x^2, let me show u how to simplify each of them quick

Answer 19

first form :-
\(\large \sqrt{x^4} = \sqrt{(x^2)^2} = \color{red}{x^2}\)


second form :-
\(\large \frac{x^5}{x^3} = \frac{x^2x^3}{x^3} = \color{red}{x^2} \)


third form :-
\(\large \frac{x^3(x-1)}{x^2-x} = \frac{x^2x(x-1)}{x(x-1)} = \color{red}{x^2}\)

Answer 20

see if they make sense

domain restrictions, id let ur teacher explain u... it will be next topic maybe :) good luck !

Answer 21

you're amazing! thank you :)

Answer 22

aww you're sweet, yu wlcme :D