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determinati x€R din ecuatia |x^2+6x+9|=|x^2+10x-11|

Răspuns :

Răspuns: ±[tex]\frac{\sqrt{202}}{8}[/tex]

Explicație pas cu pas: |x^2 +6x+9|=|x^2 +10x-11| <=> (x^2 +6x+9)^2 =(x^2 +10x-11)^2

x^4 +36x^2 +81 = x^4 +100x^2 -121

36x^2 -100x^2 = -121-81

-64x^2 = -202

x^2 = 202/64

x= ±[tex]\sqrt{\frac{202}{64}}[/tex]= ±[tex]\frac{\sqrt{202}}{8}[/tex]