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Gooday.
I'm doing some exercises and i'm stuck at one:
|x| = 12 - x^2
I need to solve this equation. Well, when i try to solve this, i get two quadratic equations:
-1(x+4)(x-3) = 0
and
(x-4)(x+3) = 0
So the answers i get are: x = -4, x = 4, x = 3, x = -3, however the book says only x = 3 and x = -3 are viable answers. I understand why this is by plugging in 3 and -3 in the first equations, however i don't understand how i should come to this conclusion computationally?
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When you solve the equation you have to get rid of | | sign.
(1) If x>0 then
x=12-x^2
Its solution is -4 0r x=3 but you have to fulfil the condition x>0 So x=3 is the only solution for this module
(2) If x<0 then
-x=12-x^2
This gives the solution x=4 or x=-3.but x<0 in this module. So x=-3 is the only solution in this module.
Combine the two.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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Oh, thank you, i forgot all about the "if" clauses.
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It is not the matter of if clause. you have to have a clear start especially for terms involving modulus or absolute as we call it. |x| to be taken as -x only if x is negative. That must be followed till solution is obtained. Here you started with |x|=-x and got 2 values 4 and -3 .You have to choose only the consistent one. mathematics is very easy if you follow simple logic and do not mix up things.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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It is not the matter of if clause. you have to have a clear start especially for terms involving modulus or absolute as we call it. |x| to be taken as -x only if x is negative. That must be followed till solution is obtained. Here you started with |x|=-x and got 2 values 4 and -3 .You have to choose only the consistent one. mathematics is very easy if you follow simple logic and do not mix up things.
I understand that, when i am learning a new subject things sometimes get a bit overwhelming, so in this case writing a clear if clause helped me to get my bearings and what it was that i was trying to do. Thank you for the answers!
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