Question

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

Answer 1

Răspuns: ±$\frac{\sqrt{202}}{8}$

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= ±$\sqrt{\frac{202}{64}}$= ±$\frac{\sqrt{202}}{8}$