Question

Rezolvati in Z ecuatiile :
a. 9(x-2)= -63
b. 5(x+3)= 2(5x-5)
c. 2(4x+1)= 2(5x-7)
d. 2(-x+5)= -8(3x+2)+56
e. 1-4*[-5(x-2)]=21
f. 2(x-2)-7(x+3)+35= 0
g. (x+3)*(x-7)=0
h. (-2x+6)*(x+3)= 0

Answer 1

Salut,

a. 9(x-2) = -63
9x-18 = -63
9x = -63+18
9x = -45
x = -45/9
x = -5.

b. 5(x+3) = 2(5x-5)
5x+15 = 10x-10
5x-10x = -10-15
-5x = -25 /•(-1)
5x = 25
x = 25/5
x = 5.

c. 2(4x+1) = 2(5x-7)
8x+2 = 10x-14
8x-10x = -14-2
-2x = -16 /•(-1)
2x = 16
x = 16/2
x = 8.

d. 2(-x+5) = -8(3x+2)+56
-2x+10 = -24x-16+56
-2x+10 = -24x+40
-2x+24x = 40-10
22x = 20
x = 20/22
x = 10/11.

e. 1-4×[-5(x-2)] = 21
1-4×(-5x+10) = 21
-4(-5x+10) = 21-1
20x-40 = 20
20x = 20+40
20x = 60
x = 60/20
x = 3.

f. 2(x-2)-7(x+3)+35 = 0
2x-4-7x-21+35 = 0
-5x-25+35 = 0
-5x+10 = 0
-5x = -10 /•(-1)
5x = 10
x = 10/5
x = 2.

g. (x+3)×(x-7) = 0
x(x-7)+3(x-7) = 0
x²-7x+3x-21 = 0
x²-4x+)-21 = 0.

a = 1
b = -4
c = -21.

∆ = b²-4ac
∆ = (-4)²-4•1•(-21)
∆ = 16+84
∆ = 100.

x1 = (-b-√∆)/2a
x1 = (4-10)/2
x1 = -6/2
x1 = -3.

x2 = (-b+√∆)/2a
x2 = (4+10)/2
x2 = 14/2
x2 = 7.


S = {-3;7}.


h. (-2x+6)×(x+3) = 0
-2x(x+3)+6(x+3) = 0
-2x²-6x+6x+18 = 0
-2x²+18 = 0
-2x² = -18
x² = -18/-2
x² = 9
x = ±√9
x = ± 3.




Succes!