wartość bezwzględna. KASIA: Rozwiąż równianie:

|x| −1		1+|x|
	−		= 0
|x|+1		1−|x|

czy mógłby ktoś chociaż podać wynik ? bo wyszło mi że nie ma rozwiązania, i chciałam się upewnić czy się nigdzie nie pomyliłam. z góry dziękuje

ula: mi też

Nikka: 1^o |x|=x

x−1		1+x
	−		= 0
x+1		1−x

D: x≠ −1 i x≠1

x−1		x+1
	+		= 0
x+1		x−1

(x−1)2 + (x+1)2
	= 0
(x+1)(x−1)

(x−1)² + (x+1)² = 0 x² −2x +1 + x² + 2x + 1 = 0 2x² + 2 = 0 /:2 x² + 1 = 0 x∊∅ bo dla każdego x∊R x²+1>0 2^o |x| = −x

−x−1		1−x
	−		= 0
−x+1		1+x

D: x≠1 i x≠ −1

x+1		x−1
	+		= 0
x−1		x+1

(x+1)2 + (x−1)2
	= 0
(x+1)(x−1)

dokładnie to samo co w 1^o czyli znowu x∊∅ Równanie nie ma rozwiązania.

KASIA: dziękuje

Marlenka: x−1 1+x = 0 x+1 1−x D: x≠ −1 i x≠1 x−1 x+1 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− + −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− = 0 x+1 x−1 (x−1)2 + (x+1)2 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− = 0 (x+1)(x−1) (x−1)2 + (x+1)2 = 0 x2 −2x +1 + x2 + 2x + 1 = 0 2x2 + 2 = 0 /:2 x2 + 1 = 0 x∊∅ bo dla każdego x∊R x2+1>0 2o |x| = −x −x−1 1−x −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− − −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− = 0 −x+1 1+x D: x≠1 i x≠ −1 x+1 x−1 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− + −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− = 0 x−1 x+1 (x+1)2 + (x−1)2 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− = 0 (x+1)(x−1)