Question

Ex 18 va rog frumos!!

Answer 1

18 ) 
a)  ( x + 2) ( x + 3) - 5 ( x + 1) = ( x - 1)² + 6 
x² + 2 x + 3 x + 6 - 5 x - 5 = x²- 2 x + 1 + 6 
x²  + 5 x - 5 x + 1 = x² - 2 x + 7 
x² - x² + 2 x = 7 - 1 
2 x = 6 ⇒ x = 6 : 2  ⇒ x = 3 

b)    3 ( x + 5 ) - ( 2x - 1)² - 13 = 5 ( 1 - x ) ( 1 + x ) + ( x - 3)²
3 x + 15 - ( 4 x² - 4 x + 1 ) - 13 = 5 ( 1 - x²) + x² - 6 x + 9 
3 x + 15 - 4 x² + 4 x - 1 - 13 = 5 - 5 x² + x² - 6 x + 9 
- 4 x² + 4 x² + 7 x + 6 x = 14 - 1 
 13 x = 13 ⇒  x = 13 : 13  ⇒ x = 1 

c)  ( 2 x - 3 ) ( 2 x + 3 ) - 4 x ( x + 1) = 2 ( x + 3) + 3 
4 x² - 9 - 4 x² - 4 x = 2 x + 6 + 3 
- 4 x - 2 x = 9 + 9 
- 6 x = 18 ⇒  x = 18 : ( - 6 )   ⇒ x = - 3 

d)  2 x ( x - 6 ) + ( x - 3) ( 2 - x) = ( x - 5 ) ( 5 + x ) - 5 ( x - 1) 
2 x² - 12 x + 2 x - 6 - x² + 3 x = x² - 25 - 5 x + 5 
2 x² - 2 x² - 7 x + 5 x = - 20 + 6 
- 2 x = - 14 ⇒  x = ( - 14 ) : ( - 2) ⇒  x = 7 

e)  ( 3 x - 5 ) ( 3 x + 5 ) - 8 x ( x - 2) = ( x + 1 ) ( x + 3) - 40 
9 x² - 25 - 8 x² + 16 x = x² + x + 3 x + 3 - 40 
9 x² - 9 x² + 16 x - 4 x = - 37 + 25 
12 x = - 12 ⇒  x = ( - 12) : ( 12 )  ⇒ x = - 1 

f) 
5 ( x - 3)² - ( 2 x - 3)² + x + 3 = 4 ( x - 2)² - 3( 1 - x)² + ???
5 ( x² - 6 x + 9 ) - ( 4 x² - 12 x + 9) + x + 3 = 4 ( x² - 4 x + 4 ) - 3 ( 1 - 2 x + x² ) + ???
5 x² - 30 x + 45 - 4 x² + 12 x - 9 + x + 3 = 4 x² - 16 x + 16 - 3 + 6 x - 3 x² + ???
x² - x² - 17 x + 10 x = 13 - 39 
- 7 x = - 26 + ?? → nu s-a vazut sfarsitul exercitiului 

g) 
( 3 x - 1)² - 5 ( x + 2) ( x - 2) + 12 = 6 + ( 2 x + 3)²
9 x² - 6 x + 1 - 5 ( x² - 4) + 12 = 6 + 4 x² + 12 x + 9 
9 x² - 6 x + 1 - 5 x² + 20 + 12 = 4 x² + 12 x + 15 
9 x² - 9 x² - 6 x - 12 x = 15 - 33
- 18 x = - 18 
x = ( - 18 ) : ( - 18) 
x = 1