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}