Question

[(3+a)x3+3x(3+3:a)]:3-3x3+3:3=2.

Answer 1

Răspuns:

$a_{1}$=1       $a_{2}$=3

Explicație pas cu pas:

[(3+a)x3+3x(3+3:a)]:3-3x3+3:3=2

I. determinăm domeniul de definiție, a≠0

[(3a)*3+3(3+3÷a)]÷3-3*3+3÷3=2

[ 9+3a+3(3+  $\frac{3}{a}$)]*$\frac{1}{3}$-9+1=2

(9+3a+9+$\frac{9}{a}$)*$\frac{1}{3}$-9+1=2

(18+3a+$\frac{9}{a}$)*$\frac{1}{3}$-9+1=2

$\frac{18a+3a^{2} }{a}$*$\frac{1}{3}$-9+1=2

$\frac{3(6a+a^{2}+3) }{a}$*$\frac{1}{3}$-9+1=2

$\frac{6a+a^{2}+3 }{a}$-9+1=2

$\frac{6a+a^{2}+3}{a}$-8-2=0

$\frac{6a+a^{2}+3}{a}$-10=0

$\frac{6a+a^{2}+3-10a }{a}$=0

$\frac{-4a+a^{2}+3 }{a}$=0

-4a+$a^{2}$+3=0

$a^{2}$-a-3a+3=0

$a^{2}-a-3a+3=0$

a(a-1)-3(a-1)=0

(a-1)(a-3)=0

a-1=0    a-3=0

a=1        a=3      a≠0

$a_{1}$=1       $a_{2}$=3

Answer 2

Răspuns:

a = 1; a = 3

Explicație pas cu pas:

a ≠ 0

[(3+a)×3 + 3×(3+3:a)]:3 - 3×3 + 3:3 = 2

[9 + 3a + 3×(3+3:a)]:3 - 9 + 1 = 2

[9 + 3a + 3×(3+3:a)]:3 = 10

9 + 3a + 3×(3+3:a) = 10×3

3a + 3×(3+3:a) = 30 - 9

3a + 3×(3+3:a) = 21 |:3

a + 3 + 3:a = 7

a + 3:a = 7 - 3

a + 3:a = 4 |×a

a² + 3 - 4a = 0

a² - 3a - a + 3 = 0

a(a - 3) - (a - 3) = 0

(a - 1)(a - 3) = 0

=>

a - 1 = 0 => a = 1

a - 3 = 0 => a = 3