Question

Oblicz x + |x| oraz x-2|x|

a) x= 4 - 2√6
b) x= 6√2 -8

Answer 1

X+|x| = x+x = 2x   gdy x>0 
x+|x| = x-x = 0  gdy x<0 

x-2|x| = x-2x = -x  gdy x>0
x-2|x|=x+2x = 3x gdy x<0 

a)  x= 4 - 2√6
 zauważ, że x<0  zatem:
x+|x| = 0 
|x|-2|x| = 3x = 3(4 - 2√6) = 6(2-√6)

b) x=6√2-8
tutaj x>0 zatem,
x+|x| = 2x = 2(6√2-8)=4(3√2-4)
x-2|x|=-x = 8-6√2 = 2(4-3√2)