2(x²+x+1)²-7(x-1)²=13(x³-1)

<=> 2(x²+x+1)²-7(x-1)²-13(x³-1)=0

<=>2(x²+x+1)²-14(x³-1)+(x³-1)-7(x-1)²=0

<=> 2(x²+x+1)(x²+x+1-7x+7)+(x-1)(x²+x+1-7x+7)=0

<=> (2x²+2x+2)(x²-6x+8)+(x-1)(x²-6x+8)=0

<=> (x²-6x+8)(2x²+3x+1)=0

<=> (x²-4x-2x+8)(2x²+2x+x+1)=0

<=> [x(x-4)-2(x-4)][2x(x+1)+(x+1)]=0

<=> (x-4)(x-2)(x+1)(2x+1)=0

Đến đây dễ rồi nhé bạn

a) với a = -2 ta được phương trình:

3.[(-2) - 2].x + 2.(-2).(x - 1) = 4.(-2) + 3

<=> 3.(-4x) - 4.(x - 1) = (-8) + 3

<=> -12x - 4(x - 1) = -5

<=> -12x - 4x + 4 = -5

<=> -16x + 4 = -5

<=> -16x = -5 - 4

<=> -16x = -9

<=> x = 9/16

b) để x = 1, ta có:

3.(a - 2).1 + 2a(1 - 1) = 4a + 3

<=> 3(a - 2) + 0 = 4a + 3

<=> 3a - 6 = 4a + 3

<=> 3a - 6 - 4a = 3

<=> -a - 6 = 3

<=> -a = 3 + 6

<=> a = -9

bn coi lại đề ik ạ

\(\frac{x+1}{9}+1+\frac{x+2}{8}+1=\frac{x+3}{7}+1+\frac{x+4}{6}+1\)

\(\Leftrightarrow\frac{x+10}{9}+\frac{x+10}{8}=\frac{x+10}{7}+\frac{x+10}{6}\)

\(\Leftrightarrow\left(x+10\right)\left(\frac{1}{9}+\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\right)=0\)

\(\Rightarrow x=-10\)

\(\frac{x^2-x}{x^2-x+1}-\frac{x^2-x+2}{x^2-x-2}=1\)

\(=\frac{x\left(x-1\right)}{\left(x-1\right)^2}+\frac{x^2-x-2}{x^2-x-2}\)

\(=\frac{x}{x-1}+1=1\)

\(\Rightarrow\frac{x}{x-1}=0\Rightarrow x=0\)

Vậy x = 0

cam on ban nhieu nha

Ta có:

$\dfrac{x^4}{2x^2+1}+\dfrac{2x^2+1}{x^4}=2$

Điều kiện: $x\ne0$.

Đặt $t=\dfrac{x^4}{2x^2+1}>0$.

Khi đó:

$t+\dfrac{1}{t}=2$

$t^2-2t+1=0$

$(t-1)^2=0$

$t=1$

$\dfrac{x^4}{2x^2+1}=1$

$x^4=2x^2+1$

$x^4-2x^2-1=0$

Đặt $y=x^2\ge0$:

$y^2-2y-1=0$

$y=1+\sqrt2$ (do $y\ge0$)

$x^2=1+\sqrt2$

$x=\pm\sqrt{1+\sqrt2}$

Vậy $x=\pm\sqrt{1+\sqrt2}$.

Ta có:

$\left(\dfrac{x}{x-1}\right)^2+\left(\dfrac{x}{x+1}\right)^2=\dfrac{10}{9}$

Điều kiện: $x\ne\pm1$.

Quy đồng:

$\dfrac{x^2(x+1)^2+x^2(x-1)^2}{(x^2-1)^2}=\dfrac{10}{9}$

$\dfrac{x^2[(x+1)^2+(x-1)^2]}{(x^2-1)^2}=\dfrac{10}{9}$

$\dfrac{2x^2(x^2+1)}{(x^2-1)^2}=\dfrac{10}{9}$

$18x^2(x^2+1)=10(x^2-1)^2$

$9x^2(x^2+1)=5(x^2-1)^2$

$9x^4+9x^2=5x^4-10x^2+5$

$4x^4+19x^2-5=0$

Đặt $t=x^2\ge0$:

$4t^2+19t-5=0$

$(4t-1)(t+5)=0$

$t=\dfrac14$ (do $t\ge0$)

$x^2=\dfrac14$

$x=\pm\dfrac12$

Vậy $x=\pm\dfrac12$.

Ta có:

$x^3+3x^2-10x-24=0$

Nhóm các hạng tử:

$x^2(x+3)-10(x+3)=0$

$(x+3)(x^2-10)=0$

$x+3=0$ hoặc $x^2-10=0$

$x=-3$ hoặc $x=\pm\sqrt{10}$

Vậy $x\in{-3,-\sqrt{10},\sqrt{10}}$.

ĐKXĐ: \(x\ne2\)

\(\frac{1}{x-2}+3=\frac{x-3}{2-x}\Leftrightarrow\frac{1}{x-2}+\frac{3x-6}{x-2}=\frac{3-x}{x-2}\Leftrightarrow3x-5=3-x\)

<=> 3x-5=3-x <=> 4x=8 <=> x=2 (loại)

Vậy pt vô nghiệm