bonjour
(E1)
x²-6x+5 =0
Δ = b² – 4 × a× c
= (-6)² - 4 × 1× 5
=36-20
=16 =4²
x1 = ( -b-√Δ)/2a
x1 =(6 -4 )/2 =2/2
=1
x2 =( -b+√Δ)/2a
x2= (6 +4 )/2 =10/2=5
S={1;5}
(E2)
3x²=15
x²=15/3
x²=5
x1=√5 x2=-√5
S={-√5;√5}
(E3)
4x²-12x+7 =0
Δ = b² – 4 × a× c
= (-12)² - 4 × 4× 7
=32
=(4√2)²
x1 = ( -b-√Δ)/2a
x1 = (12- 4√2) / 8
on simplifie par 4
=(3-√2)/2
x2 = ( -b+√Δ)/2a
x2 = (12+4√2) / 8
on simplifie par 4
=(3+√2) /2
S={(3-√2) /2 ; (3+√2) /2}
(E4)
(x+5) (2x-7) = (3x-2)(2x-7)
on factorise par 2x-7
(x+5) (2x-7) -(3x-2)(2x-7) =0
(2x-7) [(x+5)- (3x-2)] =0
(2x-7) (-2x+7)=0
= -(2x-7) (2x-7)=0
- (2x-7)² =0
2x-7 =0 =>
x= 7/2
S={7/2}
(E5)
3x² = x-4
3x² -x +4 = 0
Δ = b² – 4 × a× c
= -47
pas de solution
S=∅
(E6)
(8x-2)² =(4x-5)²
64x²-32x+4=16x²-40x+25
48x²+8x-21=0
Δ = b² – 4 × a× c
= 4096
=64²
x1 = -3/4
x2 = 7/12
S={-3/4; 7/12}
