Question

http://prntscr.com/28u0t4

Answer 1

I would help, but I can't see the problem

Answer 2

what are real solutions of the equation\[|x|^2+2|x|-3=0 ?\]

Answer 3

|x|^2 is the same as x^2
so you can split this up as 0=x^2 + 2x - 3 and 0=x^2 -2x -3

Answer 4

or you could let |x| = y
get 2 values of y
then resubstitute back y = |x|
to get 4 values of x

Answer 5

but that would give you 2 fake solutions

Answer 6

after we get 4 values,
we need to verify all 4 of them
by plugging into original question.

verification needs to be done in every problem involving absolute sign :)

Answer 7

let her calculate this values.
then we'll move ahead for verification...

Answer 8

i did the same thing

Answer 9

and what 4 values of x did u get ?

Answer 10

x^2 +2x =3 , x^2-2x= 3

Answer 11

ok
can u solve those quadratics ?

Answer 12

ax^2+bx+c=0

Answer 13

use factor method to solve both the quadratics.

Answer 14

(x+1)(x+2)

Answer 15

that would be x^2+3x+2

Answer 16

but we want to factor
x^2+2x-3

Answer 17

(x+2)(x-1)

Answer 18

second one (x-2)(x+1)

Answer 19

no....
what 2 numbers have sum as +2 and product as -3 ?

Answer 20

3-1 and for the second -3+1

Answer 21

yes!
so what are the factors ?

Answer 22

-1+1 ans -3+3

Answer 23

yes,
so 4 values of x are 1,-1,3,-3
plug them one by one, in your original equation and check for which values, do u get left side = right side

Answer 24

only 2 of those values will satisfy the original equation

Answer 25

if it is +-1 than why not +-3

Answer 26

because +3 and -3 does not satisfy original equation!
and they are called EXTRANEOUS solutions.

your actual solutions are just 1,-1

Answer 27

can you explain EXTRANEOUS solutions

Answer 28

ok, its like we fond those solutions by solving, but those solutions does not satisfy the original equation.
like if we have |x| = -3
squaring we get
x^2 = 9
x = +3, -3
but neither +3, nor -3 satisfies |x| = -3

Answer 29

can you tell me the trick how to recognize it in different questions

Answer 30

verifying is the only way to get actual solutions
plug in the solutions you get by solving, in original equations.
the solutions which satisfy it are actual solutions, and others are not.