Question

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

Answer 1

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