Question

How do you solve this equation?

Answer 1

\[|a ^{2}-2\sqrt{2} a+1|<1\]

Answer 2

removing the mod \[-1<a^2-2\sqrt{2}+1<1\]

Answer 3

do u know how to find roots

Answer 4

after factorizing
\[a=\sqrt{2} \pm 1\]

Answer 5

Wait

Answer 6

we will reject positive because -1<a<1

Answer 7

On the book it say that the results are:
\[0<a<\sqrt{2}\]
\[\sqrt{2}<a<2\sqrt{2}\]

Answer 8

omg sorry I wrote the wrong equation

Answer 9

No sorry it's the correct one

Answer 10

xD

Answer 11

But how do i get these results??

Answer 12

do u know middle splitting

Answer 13

is my answer cortrect

Answer 14

@naylah reply

Answer 15

No i don't know middle splitting

Answer 16

I already wrote the results before and yours aren't correct...
I reslly don't know how to get those results

Answer 17

do u know this formula for factorizing

Answer 18

ok

Answer 19

is the answer 0<a<2sqrt2

Answer 20

yea

Answer 21

see \[-1<a^2-2\sqrt2+1<1\]

Answer 22

after removing mod

Answer 23

any pornlem @naylah

Answer 24

problem

Answer 25

sorry misprint

Answer 26

pls reply if ur reading

Answer 27

And then how do i continue?

Answer 28

As @kanwal32 said, you must split the problem in two parts,

\[a^2-2\sqrt{2}+1<1\]
\[a^2-2\sqrt{2}+1>-1\]

Then you should solve first,

\[a^2-2\sqrt{2}+1=1\]
\[a^2-2\sqrt{2}+1=-1\]

The solutions for the first are, a=0 and a=2\sqrt{2}. For the second, a=\sqrt{2} (with multiplicity 2).

Now you can plot the graph, or evaluate numerically in the intervals you have just obtained,


----- 0 --------- 2\sqrt{2} --------- f(x)=a^2-2\sqrt{2} (the negative zones are the ones that belongs to the solution)

---------\sqrt{2}------------------f(x)=a^2-2\sqrt{2}+2 (the positive zones are the ones that belongs to the solution)

You will observe the sign of these values. The only interval where the signs are the same is the interval (0,2\sqrt{2}). You can also see in the following graph, that this is the only interval that satisfies the condition of the problem,

http://www.wolframalpha.com/input/?i=Plot [{abs[a^2+-+2+Sqrt[2]+a+%2B+1]%2C+1}%2C+{a%2C+-3%2C+3}]

(without splitting the function as before)

Answer 29

yes I forgot to make cases(I am sorry)

Answer 30

no it's not true. I don't need the graph...
I just to see why you get the results...
you resolution doesn't bring me the the solutions that I want.

Answer 31

see did with the wrong method

Answer 32

I actually understood how to do it. thanks anyways

Answer 33

\[\left| a^2-2\sqrt2+3 \right|\]