Question

Cum se rezolva exercitiile:

1) 25x la a doua + 10x +1 ( descompuneti in factori )
2) (5-x) la a doua - ( 2x+3 ) la a doua ( descompuneti in factori ) 
3) x la a doua - 13 x + 42 ( descompuneti in factori ) help meee urgent

Answer 1

1)25x²+10x+1=0
a=25
b=10
c=1
Δ=b²-4ac=10²-4·25·1=100-100=0
x₁=(-b+√Δ)2a=-10/50==-1/5
x₂=-1/5
25x²+10x+1=(x+1/5)(x+1/5)=(5x+1)(5x+1)=(5x+1)²

2)(5-x)²-(2x+3)²=25-10x+x²-(4x²+12x+9)=25-10x+x²-4x²-12x-9=
-3x²-22x+16             (-1)
3x²+22x-16=0
Δ=484+192=676
x₁=(-22+26)/6=4/6=2/3
x₂=(-22-26)/6=-48/6=-8
3x²+22x-16=(x-2/3)(x+8)=(3x-2)(x+8)

3) x²-13x+42=0
Δ=169-168=1
x₁=(13-1)/2=12/2=6
x₂=(13+1)/2=14/2=7
x²-13x+42=(x-6)(x-7)