Question

Rezolvati ecuatiile urmatoare:
a) (x-1)(x+1)+2x=(x-4)²+3
b) (5-x)(x+5)=4-x(x+3)
c) (2x+3)²+5=(2x+3)(2x-3)-1
d) x+1/5+2x=3x/2-4
e) x+3/5+x-1/2=2x+17

Answer 1

a) (x-1)(x+1)+2x=(x-4)²+3
x²-1+2x=x²-8x+16+3
-1+2x=-8x+19
-1+2x+8x-19=0
10x-20=0=>10x=20=>x=2

b) (5-x)(x+5)=4-x(x+3)
5x+25-x²-5x=4-x²-3x
25=4-3x
21=-3x=>x=-7

c) (2x+3)²+5=(2x+3)(2x-3)-1
4x²+12x+9+5=4x²-9-1
12x+14=-10
12x=-24=>x=-2

d) x+1/5+2x=3x/2-4
3x+1/5=-3x/2
Aducem,la,numitor,comun(10)
30x+2=-15x
30x+15x=-2
45x=-2=>x=-2/45

e)x+3/5+x-1/2=2x+17
2x+3/5-1/2=2x+17
Ecuatia,nu,are,solutii.

Answer 2

(x-1)(x+1)+2x=(x-4)²+3
x^2+2x−1=x^2−8x+19
10x=20
x=2

(5-x)(x+5)=4-x(x+3)
−x^2+25=−x^2−3x+4
−3x=21
x=−7

(2x+3)²+5=(2x+3)(2x-3)-1
4x^2+12x+14=4x^2−10
12x=−24
x=−2

x+1/5+2x=3x/2-4
3x+1/5=3x/2-4
30x+2=15x-40
15x=-42
x=-42/15
x=-14/5

(x+3)/5+(x-1)/2=2x+17
2(x+3)+5(x-1)=10(2x+17)
7x+1=20x+170
−13x=169
x=−13