Question

1) Determinati x ∈ R pentru care sunt adevarate egalitatile:
a) x(x+1)=x+2=?
b) (x +3)(x-3)=5-(x+2)(x-2)=?

2) Aratati ca ecuatiile urmatoare sunt echivalente:
x(2x+1)+(x+1)(x+2)=2(x²+11)+1 si 2(x+1)²-(x-2)(x+2)=27
REPEDE VA ROG
DAU PUNCTE SI CORONITE

Answer 1

1a) x²+x=x+2
x²+x-x=2
x²=2
x₁=√2
x₂=-√2
(√2)²+√2=√2+2
2+√2=2+√2
S={√2,-√2)

b)(x+3)(x-3)=5-(x+2)(x-2)
x²-9=5-x²+4
x²+x²=5+4+9
2x²=18
x²=18/2
x²=9
x₁=√9=3
x₂=-√9=-3
(3+3)(3-3)=5-(3+2)(3-2)
6·0=5-5
0=0
S={-3,3}

2)x(2x+1)+(x+1)(x+2)=2(x²+11)+1
2x²+x+x²+2x+x+2=2x²+22+1
3x²-2x²+4x-22-1+2=0
x²+4x-21=0

si2(x+1)²-(x-2)(x+2)=27
2(x²+2x+1)-x²+4=27
2x²+4x+2-x²+4-27=0
x²+4x-21=0
cele 2 ec.sunt echivalente