How would you end up solving, |2-|1-|x||| = 1,
i realize the basic idea but what do you do with the negative after the 2, do you distribute it?
edit: through the powers of trial and error i found
that you dont need to distribute but rather just divide the -1 and the answers are, +-4, +-2, and 0.
| 2−| 1−|x| | |=1|square both sides( 2−| 1−|x| | )2=124−4⋅| 1−|x| |+(1−|x|)2=14−4⋅| 1−|x| |+⧸1−2|x|+x2=⧸14−4⋅| 1−|x| |−2|x|+x2=0x2−2|x|+4=4⋅| 1−|x| ||square both sides(x2−2|x|+4)2=16⋅( 1−|x| )2(x2−2|x|+4)⋅(x2−2|x|+4)=16⋅( 1−2|x|+x2 )x4−4|x|⋅x2+12x2−16x+⧸16=⧸16−32⋅|x|+16x2x4−4|x|⋅x2+12x2−16x=−32⋅|x|+16x2x4−4|x|⋅x2+16|x|−4x2=04|x|⋅(4−x2)=4x2−x44|x|⋅(4−x2)=x2⋅(4−x2)|square both sides16x2⋅(4−x2)2=x4⋅(4−x2)216x2⋅(4−x2)2−x4⋅(4−x2)2=0(4−x2)2⋅(16x2−x4)=0(4−x2)2⋅x2⋅(16−x2)=0(4−x2)⋅(4−x2)⋅x⋅x⋅(16−x2)=0
1.
4−x2=0x2=4x=±√4x1=2x2=−2
2.
x=0⇒x3=0
3.
16−x2=0x2=16x=±√16x4=4x5=−4
