Question

Rezolvati ecuatiile :
1) (x+ √3)(x-√3)=24
2) x la a doua supra √11 -√7= √11+√7
3)(x-√6) la a doua = 24
4) 3(x+1/3) la a doua + 2/3 =9
5)(x-3) la a doua =3(9x-2x)
6)6x(5x+3)=18
7) 2-1/x=3-2/x+1
8) x la a doua +4x / 4 = x la a doua + 5x / 5
Ajutati-ma , va rog .

Answer 1

1) (x+ √3)(x-√3)=24
x²-3=24
x²=27
x=+/-√27
x=+/-3√3

2) x² √11 -√7= √11+√7
x²=( √11+√7+√7)/√11
x²=( √11+2√7)/√11
x²=1+2√7/√11
x²=1+2√77/11
x=+/-√(1+2√77/11)

3)(x-√6)² = 24
x²-2x√6+6 = 24
x²-2x√6-18 =0
a=1
b=-2√6
c=-18
Δ=b²-4ac=24+72=96
x₁=(2√6+√96)/2=(2√6+4√6)/2=3√6
x₂=(2√6-√96)/2=(2√6-4√6)/2=-√6

4) 3(x+1/3)² + 2/3 =9
3(x²+2x/3+1/9)+2/3=9
3x²+2x+1/3+2/3=9
3x²+2x+1-9=0
3x²+2x-8=0
a=3
b=2
c=-8
Δ=b²-4ac=4+96=100
x₁=(-2+√100)/6=(-2+10)/6=4/3
x₂=(-2-√100)/6=(-2-10)/6=-2

5)(x-3)² =3(9x-2x)
x²-6x+9 =21x
x²-28x+9 =
a=1
b=-28
c=9
Δ=b²-4ac=784+36=748
x₁=(28+√748)/2=(28+2√187)/2=14+√187
x₂=(28-√748)/2=(28-2√187)/2=14-√187

6)6x(5x+3)=18
30x²+18x-18=0
15x²+9x-9=0
a=15
b=-9
c=-9
Δ=b²-4ac=36+540=576
x₁=(9+√576)/30=(9+24)/30=33/30=11/10
x₂=(9-√576)/30=(9-24)/30=-15/30=-1/2


7) 2-1/x=3-2/x+1
 1/x=3+1-2
1/x=2
x=0,5

8) x² +4x / 4 = x² + 5x / 5
 x  = x 

sau
( x² +4x) / 4 =( x² + 5x) / 5
5x² +20x =4 x² + 20x 
5x²  =4 x²
x²  =0
x=0