Question

rezolvati in multimea numerelor reale ecuatia 2x-1 supra 3x-2 = 4x+3 supra 6x+5

Answer 1

$\frac{2x-1}{3x-2}= \frac{4x+3}{6x+5} \\   x\neq\frac{2}{3}, x\neq \frac{5}{6}$

Inmultesti pe diagonala

(2x-1)*(6x+5)=(4x+3)*(3x-2)=

$12x^{2} +10x-6x-5=12x^{2} -8x+9x-6$  

$12x^{2}+10x-6x-5-12x^{2} =-8x+9x-6\\10x-6x-5=-8x+9x-6\\4x-5=x-6\\4x-x=-6+5\\3x=-1\\x=\frac{1}{3}$

Answer 2

( 2 x - 1 ) / (  3x - 2 ) = ( 4 x + 3 ) / ( 6 x + 5 )

⇒ ( 2 x - 1 ) ( 6 x + 5 ) = (3 x - 2 ) ( 4 x + 3 )

           ⇒produsul mezilor = produsul extremilor

12 x² - 6 x + 10 x - 5 = 12 x² - 8 x + 9 x - 6

12 x² + 4 x - 5 = 12 x² + x - 6

12 x² + 4 x - 12 x² - x = - 6 + 5

3 x = - 1

x = - 1 / 3