Question

Rezolvati in R ecuatiile:
1.
a)(x+1)(x+1)-x (la puterea 2)=x-1
b)(y+1)(y+2)+2y+1=y (la puterea 2)+4y
c)(t+1)(t-2)-t(t-3)=1
d)z (la puterea 2) -z-z(z+2)=3z-4
2.
a)(x+1)(la puterea 2) =(x+2)(la puterea 2)-5
b)(2u+3)la puterea 2-(2u-1)(la puterea 2)=12u+8
c)(t+1)(la puterea 2)-(t-3)(la puterea2)
d)6x(2x+3)-4(x+1)(x-1)=2(2x-1)(la puterea 2)-11
3.
(x√2+1)(la puterea 2)+x(x-4√3)=(x√3-2)(la puterea 2)

Answer 1

a)(x+1)(x+1)-x²=x-1
x²+2x+1-x²=x-1
2x+1=x-1
x=-2

b)(y+1)(y+2)+2y+1=y²+4y
y²+y+2y+2+2y+1=y²+4y
+y+2+1=0
y=-3

c)(t+1)(t-2)-t(t-3)=1
t²+t-2t-2-t²+3t=1
2t=3
t=3/2


d)z²-z-z(z+2)=3z-4
z²-z-z²-2z=3z-4
-z-2z=3z-4
6z=4
z=2/3

2.
a) (x+1)² =(x+2)²-5
x²+2x+1=x²+4x+4-5
+1=2x-1
2x=2
x=1


b)(2u+3)²-(2u-1)²=12u+8
(2u+3)²-(2u-1)²=12u+8
4u²+12u+9-4u²+4u-1=12u+8
+9+4u-1=+8
4u=0
u=0


c)(t+1)²-(t-3)²  =???????


d)6x(2x+3)-4(x+1)(x-1)=2(2x-1)²-11
12x²+18x-4x²+4=2(4x²-4x+1)-11
8x²+18x+4=8x²-8x+2-11
+18x+4=-8x-9
26x=-13
x=-1/2

3.
(x√2+1)²+x(x-4√3)=(x√3-2)²
2x²+1+2x√2+x²-4x√3=3x²+4-4x√3
+1+2x√2-4x√3=+4-4x√3
+2x√2=+4-1
x(2√2=3
x=3/2√2=3√2/4