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Rezolvati in R ecuatiile:
a)[tex] \frac{5}{x-1} [/tex] = [tex] \frac{x-1}{45} [/tex]
b) [tex] \frac{3x-2}{3} [/tex] = [tex] \frac{147}{3x-2} [/tex]


Răspuns :

Produsul extremilor este egal cu produsul mezilor.

a) 5*45=(x-1)^2 => 225=x^2-2x+1 => x^2-2x-224=0 
Δ=4+4*224=900
x1=(2+30)/2=32/2=16
x2=(2-30)/2=-28/2=-14

b)3*147=(3x-2)^2 =>441=9x^2-12x+4 => 9x^2-12x-437=0 
Δ=144+4*9*437=15876
x1=(12+126)/18=148/18
x2=(12-126)/18=114/18