Question

Determina numarul real a pentru care urmatoarele ecuatii cu necunoscuta x au solutia 2.
a) a x +4=0
b)3 x - 4 a=0
c)(a-3)x+2 a=2
d)(2 a - 3) x + a - 4= 3 a

Answer 1

Răspuns:

Explicație pas cu pas:

a) x = 2

a x + 4 = 0

a × 2 + 4 = 0

2 a = - 4

a = ( - 4) : 2

a = - 2 ∈ R

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b)  

3 x - 4 a = 0

3 × 2 - 4 a = 0

6 - 4 a = 0

- 4a = - 6

a = ( - 6) : ( - 4 )

a = 3/2

Verific:   3 × 2 - 4 × 3/2 = 6 - 12/2 = 6 - 6 = 0

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c)

( a - 3 ) x + 2 a = 2

( a - 3 ) × 2 + 2 a = 2    

2 a - 6 + 2 a = 2

4 a = 2 + 6

4 a = 8

a = 8 : 4

a = 2

Verific:

( 2 - 3 ) × 2 + 2 × 2 = - 2 + 4 = 2

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d)

( 2 a - 3 ) x + a - 4 = 3 a

( 2 a - 3 ) × 2 + a - 3 a = 4

4 a - 6 - 2 a = 4

2 a = 4 + 6

a = 10 : 2

a = 5

Verific:  

( 2 × 5 - 3 ) × 2 + 5 - 4 = 7 × 2 + 1 = 15 √ ( 3 × 5 = 15 )