Question

Rezolvati ecuatiile:

a). (x-1)^2=9
b). 3-(x-5)^2=1
c). (3-x)(3+x)-6=2
d). 5-(x-2)(x+2)=3
e). x^2-2x+1=7
f). 4x^2-4x+1=5

Rezolvare pt. clasa a saptea multumesc dau coroană!

Answer 1

a)
(x-1)² = 9
x-1 = √9
x-1 = 3
x = 3+1
x = 4

b)
3-(x-5)² = 1
-(x-5)² = 1-3
-(x-5)² = -2 /:(-1)
(x-5)² = 2
x-5 = √2
x = √2+5

c)
(3-x)(3+x)-6 = 2
(3-x)(3+x) = 2+6
(3-x)(3+x) = 8
3²-x² = 8
9-x² = 8
9-8 = x²
x= √1
x= 1

d)
5-(x-2)(x+2) = 3
5-x²-2² = 3
5-x²-4 = 3
5-4-x² = 3
1-x² = 3
-x² = 3-1
-x² = 2
x² = -2
x = √(-2)

e)
x²-2x+1 = 5
(x-1)² = 5
x-1 = √5
x = √5+1

f)
4x²-4x+1 = 5
(2x-1)² = 5
2x-1 = √5
2x = √5+1
x = (√5+1) / 2


La câteva suppuncte nu m-am descurcat... dar sper că te-am ajutat (rimă) :)