Question

aflati numarul natural x astfel incat urmatoarele egalitati sa fie devarata: a) $\frac{3}{5}$ = $\frac{x}{10}$ b) $\frac{x+2}{x+7}$ = $\frac{3x+6}{48}$

Answer 1

$\frac{3}{5}= \frac{x}{10}$

Facem produsul mezilor = cu produsul extremilor

[tex]5x=30 [/tex]

$x= \frac{30}{5}=6$


La b tot la fel facem

[tex]48(x+2)=(x+7)(3x+6) 48x+96=3x^2+6x+21x+42 48x+96-3x^2-6x-21x-42=0 -3x^2+21x+54=0 /(-1) [/tex]

[tex]3x^2-21x-54=0 a=3 b=-21 c=-54 delta=b^2-4ac = (-21)^2-4*3*(-54) =441+648=1089 [/tex]


[tex]x1= \frac{21+33}{6}= \frac{54}{6}= 9 [/tex]


$x2= \frac{21-33}{6}= \frac{-12}{6} =-2$