Réponse :
A(x) = 4x²-100 = a²-b² qu'on factorise (a-b)(a+b)
(2x-10)(2x+10)
B(x) = (5x+1)(1-2x)+(5x+1)(1-3x)
(5x+1)(1-2x+1-3x)=
(5x+1)(-5x+2)
C(x) = (x-3)²= (a-b)²a²-2ab+b²
x²-6x+9
A(x) = 0
(2x-10)(2x+10)=0
2x-10=0⇔2x=10⇔x=10/2=5
2x+10=0⇔2x=-10⇔x=-10/5=-5
A(x) = 4x²-100=69
4x²-100-69=0
4x²-169 = (2x-13)(2x+13)=0
tu resous comme le precedent
B(x)=0
(5x+1)(-5x+2)=0
5x+1=0⇔5x=-1⇔tu finis
comme A(x)=0
6)4(x-3)²=4x²-100
4(x-3)²-(4x²-100)=0
[2(4x-3)-(2x-10)][2(4x-3)+(2x-10)]=0
(8x-6-2x+10)(8x-6+2x+10)=0
(4x+6)(10x+16)
4x+6=0⇔4x=-6⇔x=-6/4=-3/2
10x+16=0⇔10x=-16⇔x=-16/10=-8/5
Explications étape par étape
Réponse :
Bonjour,
1) A(x) = 4x² – 100
= (2x)² – 10²
= (2x + 10)(2x – 10)
= 2(x + 5) × 2(x – 5)
= 4(x + 5)(x – 5)
2) B(x) = (5 + x)(1 – 2x) + (5 + x)(1 – 3x)
= (5 + x)[(1 – 2x) + (1 – 3x)]
= (5 + x)(1 – 2x + 1 – 3x)
= (5 + x)(–5x + 2)
3) C(x) = (x – 3)²
= x² – 2 × x × 3 + 3²
= x² – 6x + 9
4) A(x) = 0
⇔ 4(x + 5)(x – 5) = 0
Or A × B = 0 ⇔ A = 0 ou B = 0
x + 5 = 0
x = –5
x – 5 = 0
x = 5
Donc S = {–5 ; 5}
A(x) = 69
⇔ 4x² – 100 = 69
⇔ 4x² = 169
⇔ x² = 169/4
⇔ x = √169/4
⇔ x = 6,5
5) B(x) = 0
⇔ (5 + x)(–5x + 2) = 0
Or A × B = 0 ⇔ A = 0 ou B = 0
5 + x = 0
x = – 5
–5x + 2 = 0
–5x = –2
x = 2/5
Donc S = {–5 ; 2/5}
6) 4x² – 100 = 4(x² – 6x + 9)
4x² – 100 = 4x² – 24x + 36
4x² – 4x² + 24x = 36 + 100
24x = 136
x = 136/24
x = 17/3