Question

14. Determinați soluţiile ecuațiilor:
a) (x+1)(x - 1) = x² + 5x+4; b) (x - 2)² – (x+1)² = x-4;
c) (2x + 3)² +7= 4(x - 2)2; d) (3x – 4)² + 20 = 5(x+1)² + (2x-3):
e) (x + 2)(3x +2) - 3x = 2x2 + (x + 1);
D x(x + 2) - (2x+3)(3x + 4) =18-5x.
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Answer 1

Răspuns:

a)x^2 - 1 = x^2 + 5x + 4

-1 = 5x + 4

-5 = 5x

x = (-1)

b)x^2 - 4x + 4 - x^2 - 2x - 1 = x - 4

-6x + 3 = x - 4

-7x = -7

x = 1

c)4x^2 + 12x + 9 + 7 = 4x^2 - 16x + 16

12x = -16x

28x = 0

x = 0

d)9x^2 - 24x + 16 + 20 = 5x^2 + 10x + 5 + 4x^2 - 12x + 9

-24x + 36 = -2x + 14

-22x = -22

x = 1

e)3x^2 + 8x + 4 - 3x = 2x^2 + x^2 + 2x + 1

5x + 4 = 2x + 1

3x = -3

x=(-1)

f)x^2 + 2x - 6x^2 - 17x - 12 = 18 - 5x^2

-15x - 12 = 18

-15x = 30

x = (-2)