Question

Ajutatima va rog la problemele urmatoare. A)x+1/4=3/4. B)4/5-x=1/2. C)5/2-x=1/4. D)x patrat -4x+4. E)9xpatrat+6x+1. F)xpatrat-8x+16. G)2xpatrat +20x+4. H)16xpatrat-8x+1. Dau coroana!!!!

Answer 1

a ) 
x + 1 / 4 = 3 / 4
x = 3 / 4 - 1 / 4
x = ( 3 - 1 ) / 4 ⇒ x = 2 / 4 ⇒ x = 1 / 2

b)
4 / 5 - x = 1 / 2
-x = 1 / 2 - 4 / 5
-x = ( 5 - 8 ) / 5
-x = -3 / 5 | · ( - 1 ) ⇒ x = 3 / 5

c)
5 / 2 - x = 1 / 4
-x = 1 / 4 - 5 / 2
-x = ( 1 - 10 ) / 4
-x = -9 / 4 | · ( - 1 ) ⇒ x = 9 / 4

d)
x² - 4x + 4 = ( x - 2 ) ² 
( x - 2 ) ² = 0 ⇒ x - 2 = 0 ⇒ x = 2

e)
9x² + 6x + 1 = 0
Δ = 6² - 4·9 = 36 - 36 = 0 
x₁ = x₁ = ( -6 + 0 ) / 18 = -6 / 18 = -1 / 3

f)
x² - 8x + 16 = ( x - 4 ) ²
( x - 4 )² = 0 ⇒ x - 4 = 0 ⇒ x = 4

g)
2x² + 20x + 4 = 0 | : 2
x² + 10x + 2 = 0
Δ = 10² - 4 · 2 = 100 - 8 = 92 ( nu este patrat perfect )

h)
16x² - 8x + 1 = ( 4x - 1 ) ²
( 4x - 1 ) ² = 0 ⇒ 4x - 1 = 0 ⇒ x = 1 / 4

Answer 2

a)
x + 1 / 4 = 3 / 4 
x = 3 / 4 - 1 / 4 
x = 2 / 4 
x = 1 / 2 

b) 
4 / 5 - x = 1 / 2 
x = 4 / 5 - 1 / 2 → le aduc la acelasi numitor comun 2 × 5 = 10 
x = 8 / 10 - 5 / 10 
x = 3 / 10 

V:    4 / 5 - 3 / 10 = 8 / 10 - 3 / 10 = 5 / 10 = 1 / 2 

c) 
5 / 2 - x = 1 / 4 
x = 5 / 2 - 1 / 4 → le aduc la acelasi numitor comun 4 
x = 10 / 4 - 1 / 4 
x = 9 / 4 

V:   5 / 2 - 9 / 4 = 10 / 4 - 9 / 4 = 1 / 4 

d) 
x² - 4 x + 4 = ( x - 2)² 
x² - 4 x + 4 = 0 
Δ = 16 - 16 = 0 ⇒ x₁= x₂= 4 / 2 =  2 

e) 
9 x² + 6 x + 1 = ( 3 x + 1) ² ⇒  x₁ = x₂ = - 1 / 3 

g) 
2 x² + 20 x + 4 = x² + 10 x + 2 = 0 
Δ = 100 - 8 = 92 
x₁ = (-10 + 2√23 )/ 2 = - 5 +√23 
x₂ = - 5 - √ 23

h) 
16 x² - 8 x + 1 = ( 4 x - 1)²
16 x² - 8 x + 1 = 0 
Δ= 0 = > x₁ = x₂ = 1 / 4