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Sagot :

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

MPOWER

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

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