Question

Rezolvati ecuatiile :
a) (x+2) la puterea 2 = 16
b) | x-3 | = 6
c) ( x-√3 ) la puterea 2 = 4 + 2√3
d) (x-5) (x+5) - (x-3) la puterea 2 = x-9
e) (x+2) la puterea 2 - x(x+5) = 2(x-7)
f) 2(x+2) + √x la puterea 2 - 4x + 4 = 2x+9

Answer 1

a) (x+2) la puterea 2 = 16
(x+2) la puterea 2 = 4 la puterea 2
x+2 = 4 => x = 2
b) | x-3 | = 6
| x | = + sau - 9
c) ( x-√3 ) la puterea 2 = 4 + 2√3
x^2 - 2√3x +3 = 4+2√3
x^2 -4√3x +3 = 0
Delta =(-4√3)^2 - 4*3
Delta = 48 -12
Delta = 36
x_1 = (4√3+6)/2
x_1= 2(2√3 + 3)/2
x_1 = 2√3+3
x_2 = (4√3-6)/2
x_2= 2(2√3 - 3)/2
x_2= 2√3-3
d) (x-5) (x+5) - (x-3)^2 = x-9
x^2 -25 -x^2 -6x +9 - x +9 = 0
-7x -7=0
-7x = 7
7x = -7
x = -1
e) (x+2)^2 - x(x+5) = 2(x-7)
x^2 +4x +4 - x^2 -5x = 2x-14
-x + 4 = 2x -14
-3x = -18
3x = 18
x = 6
f) 2(x+2) + √x^ 2 - 4x + 4 = 2x+9
2x + 4 + x -4x + 4 = 2x+9
-3x +8 = 9
-3x = 1
3x = -1
x = -1/3

Sper ca te-am ajutat.