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anonymous
 one year ago
ques
anonymous
 one year ago
ques

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why is sqrt{x^2}=x?? let f(x)=sqrt{x^2} g(x)=x h(x)=x at x= 1 we have f(x)=plus minus 1 g(x)=1 h(x)=1 clearly it looks like sqrt{x^2}=plus minus x sorry my equation box is giving errors right now so im using this

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435127988303:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Also dw:1435128205480:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435128362002:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3we could say the "2nd roots of 4" are "+2 and 2" as both of them when rised to 2nd power give us 4; but if we stick to the definition of sqrt function, we only pick the positive root.

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1@Nishant_Garg what is x^2 range ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm confused, doesn't square rooting gives 2 values?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3By definition, sqrt(x) is always the positive root of x

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3sqrt(x) is a single valued function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't understand, that sounds really really wrong

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3do you have definition of sqrt(x) function wid you ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, idk, I've been doing plus minus x all the time for sqrt of x^2 How do you suppose the equation x^2=4 has 2 solutions then if u only take the positive value?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[x^2=4 \implies x = \pm \sqrt{~4~} = \pm 2\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[x^2 =3 \implies x=\pm\sqrt{3} \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3i think you're confusing sqrt(x) function with the complex roots of x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is melting my brain, it feels like I've been square rooting wrong the whole time... so is x^2=4 different from x=sqrt{4} ??

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes they are not same. \[x = \sqrt{4} \implies x^2=4\] but the converse is not true.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[x^2=4 \implies x=\color{red}{\pm}\sqrt{4}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and x=sqrt{4} implies x=2 ONLY ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3there wont be any confusion if we take the definition seriosuly and stick to it

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3that is correct \[x=\sqrt{4}\implies x=2\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yep. sqrt(x) is never negative

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This is just bizzare, I always thought sqrt gives plus minus.....It all looks like a different point of view now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then the equation x^2=4 is to be solved like sqrt{x^2}=sqrt{4} implies x=2(by definition of sqrt) removing the mod, x=plus minus 2 but for the equation x=sqrt{4} we have x=2(by definition of sqrt)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Haha ikr! one not so cool thing about mathematics is sometimes we just need to follow rules and stick to definitions even though they seem unintuitive

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3that looks good to me!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the plus minus is a consequence of the modulus function and not square root

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3modulus function is a consequence of sqrt

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435129510602:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3as you said x=2 has two solutions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0makes sense now but feels a little different :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3since we're messing with roots, notice that below is perfectly okay : dw:1435129597807:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3but below is wrong : dw:1435129708335:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes! x^7 or x^7 both are fine

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as it has an odd power it can gives negative numbers

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Exactly! which changes the original function sqrt(x^14) as x^14 is always positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0amazing thanks a lot...
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