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rezolvați in R ecuatiile; a)|x|=4 b)|x|=√5 c)|x-1|=√2​

Răspuns :

a).

|x|=4

x=-4

x=4 ∈ R

b).

|x|=√5

x=√5 ∈ R

x=-√5 ∈ R

c).

|x-1|=√2​

x-1=√2​

x=√2​+1 ∈ R

x-1=-√2​

x=-√2​+1 ∈ R

sper ca te-am ajutat

a)|x|=4

[tex] x_{1} = 4 \\ \\ x_{2} = - 4 \\ \\ [/tex]

b)|x|=[tex] \sqrt{5} [/tex]

[tex] x_{1} = - \sqrt{5} \\ \\ x_{2} = \sqrt{5} [/tex]

c)|x-1|=[tex] \sqrt{2} [/tex]

x-1=[tex] \sqrt{2} [/tex]

x-1+1=[tex] \sqrt{2} [/tex]+1

x=[tex] \sqrt{2} [/tex]+1

x-1=-[tex] \sqrt{2} [/tex]

x-1+1=-[tex] \sqrt{2} [/tex]+1

x=-[tex] \sqrt{2} [/tex]+1

[tex] x_{1} = - \sqrt{2} + 1 \\ \\ x_{2} = \sqrt{2} + 1 [/tex]