Tìm x a) (x – 3)^3 – (x – 3) (x^2 + 3x + 9) + 9(x + 1)^2 =15 b) x(x – 5) (x + 5) – (x – 2) (x^2 + 2x +4) = -17 25/08/2021 Bởi Reagan Tìm x a) (x – 3)^3 – (x – 3) (x^2 + 3x + 9) + 9(x + 1)^2 =15 b) x(x – 5) (x + 5) – (x – 2) (x^2 + 2x +4) = -17
Đáp án: $a) \dfrac{2}{15}\\b)x=-1$ Giải thích các bước giải: $a) (x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15\\\Leftrightarrow x^3-3.x^2.3+3.x.3^3-27-(x^3-3^3)+9(x^2+2x+1)=15\\\Leftrightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15\\\Leftrightarrow 45x=15-9=6\\\Leftrightarrow x=\dfrac{2}{15}\\b)x(x-5)(x+5)-(x-2)(x^2+2x+4)=-17\\\Leftrightarrow x(x^2-25)-(x^3-2^3)=-17\\\Leftrightarrow x^3-25x-x^3+8=-17\\\Leftrightarrow -25x=-17-8=25\\\Leftrightarrow x=-1$ Bình luận
a) (x – 3)^3 – (x – 3) (x^2 + 3x + 9) + 9(x + 1)^2 =15 (=) (x^3-9x^2+27x-27)-(x^3-27)+9(x^2+2x+1)=15 (=) x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15 (=) 45x+9=15 (=) 45x=6 (=) x=6/45=2/15 Vậy x=2/15 b) x(x – 5) (x + 5) – (x – 2) (x^2 + 2x +4) = -17 (=) x(x^2-25)-(x^3-8)=-17 (=) x^3-25x-x^3+8=-17 (=) -25x+8=-17 (=) -25x=-25 (=) x=1 Vậy x=1 Bình luận
Đáp án:
$a) \dfrac{2}{15}\\
b)
x=-1$
Giải thích các bước giải:
$a) (x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15\\
\Leftrightarrow x^3-3.x^2.3+3.x.3^3-27-(x^3-3^3)+9(x^2+2x+1)=15\\
\Leftrightarrow x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15\\
\Leftrightarrow 45x=15-9=6\\
\Leftrightarrow x=\dfrac{2}{15}\\
b)
x(x-5)(x+5)-(x-2)(x^2+2x+4)=-17\\
\Leftrightarrow x(x^2-25)-(x^3-2^3)=-17\\
\Leftrightarrow x^3-25x-x^3+8=-17\\
\Leftrightarrow -25x=-17-8=25\\
\Leftrightarrow x=-1$
a) (x – 3)^3 – (x – 3) (x^2 + 3x + 9) + 9(x + 1)^2 =15
(=) (x^3-9x^2+27x-27)-(x^3-27)+9(x^2+2x+1)=15
(=) x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15
(=) 45x+9=15
(=) 45x=6
(=) x=6/45=2/15
Vậy x=2/15
b) x(x – 5) (x + 5) – (x – 2) (x^2 + 2x +4) = -17
(=) x(x^2-25)-(x^3-8)=-17
(=) x^3-25x-x^3+8=-17
(=) -25x+8=-17
(=) -25x=-25
(=) x=1
Vậy x=1