tìm x biết
1.(x-3)^3 -(x-3)(x^2+3x+9)+9(x+1)^2=15
2.x(x-5)(x+5)-(x+2)(x^2-2x+4)=3
3.(x+4)(x^2-4x+16)-x(x-5)(x+5)=264
4.(x-2)^3-(x-2)(x^2+2x+4)+6(x-2)(x+2)=60
5.(5x-1)^2-(5x-4)(5x+4)=7
tìm x biết
1.(x-3)^3 -(x-3)(x^2+3x+9)+9(x+1)^2=15
2.x(x-5)(x+5)-(x+2)(x^2-2x+4)=3
3.(x+4)(x^2-4x+16)-x(x-5)(x+5)=264
4.(x-2)^3-(x-2)(x^2+2x+4)+6(x-2)(x+2)=60
5.(5x-1)^2-(5x-4)(5x+4)=7
Đáp án:
ở dưới
Giải thích các bước giải:
$1. ( x – 3)^3 – ( x -3)(x^2 + 3x + 9) + 9( x + 1)^2 = 15$
$⇔ x^3 – 9x^2 + 27x – 27 – x^3 + 27 + 9x^2 + 18x + 9 = 15$
$⇔45x = 6$
$⇔x = 2/15$
$2. x(x – 5)(x + 5)- (x +2)(x^2 -2x +4) = 3$
$⇔ x.(x^2 – 25) – ( x^3 + 8) = 3$
$⇔ x^3 – 25x – x^3 – 8 = 3$
$⇔ – 25x = 11$
$⇔ x = -11/25$
$3. (x + 4)( x^2 – 4x + 16) – x(x – 5)(x +5) = 264$
$⇔ x^3 + 64 – x( x^2 – 25) = 264$
$⇔ x^3+ 64 – x^3 + 25x = 264$
$⇔ 25x = 200$
$⇔ x = 8$
$4. (x – 2)^3 – (x – 2)(x^2 + 2x + 4) + 6(x – 2)( x + 2) = 60$
$⇔x^3 – 6x^2 + 12x – 8 – x^3 + 8 + 6x^2 – 24 = 60$
$⇔12x = 84$
$⇔x = 7$
$5. ( 5x – 1)^2 – ( 5x – 4)(5x + 4) = 7$
$⇔ 25x^2 – 10x + 1 – 25x^2 + 16 = 7$
$⇔- 10x = -10$
$⇔ x = 1 $
Đáp án:
Giải thích các bước giải:
1. ( x – 3)³ – ( x -3)(x² + 3x + 9) +
9( x + 1)² = 15
<=> x³ – 9x² + 27x – 27 – (x³ – 27 )+ 9(x² + 2x + 1) = 15
<=> x³ – 9x² + 27x – 27 – x³ + 27 + 9x² + 18x + 9 = 15
<=> 45x + 9 = 15
<=> 45x = 6
<=> x = 2/15
Vậy x = 2/15
2. x(x – 5)(x + 5)- (x +2)(x² -2x +4) = 3
<=> x(x² – 25) – ( x³ + 8) = 3
<=> x³ – 25x – x³ – 8 = 3
<=> – 25x = 11
<=> x = -11/25
Vậy x = – 11/25
3. (x + 4)( x² – 4x + 16) – x(x – 5)
(x +5) = 264
<=> x³ + 64 – x( x² – 25) = 264
<=> x³ + 64 – x³ + 25x = 264
<=> 25x = 200
<=> x = 8
Vậy x = 8
4. (x – 2)³ – (x – 2)(x² + 2x + 4) + 6(x – 2)( x + 2) = 60
<=> x³ – 6x² + 12x – 8 – ( x³ – 8) +
6(x² – 4) = 60
<=> x³ – 6x² + 12x – 8 – x³ + 8 + 6x² – 24 = 60
<=> 12x – 24 = 60
<=> 12x = 84
<=> x = 7
Vậy x = 7
5. ( 5x – 1)² – ( 5x – 4)(5x + 4) = 7
<=> 25x² – 10x + 1 – 25x² + 16 = 7
<=> – 10x + 17 = 7
<=> – 10x = -10
<=> x = 1
Vậy x = 1