\(\left(2x-1\right)^3-8\left(x-1\right)\left(x^2+x+1\right)+12x^2=2x+1\)

\(\Leftrightarrow8x^3-12x^2+6x-1-8\left(x^3-1\right)+12x^2-2x-1=0\)

\(\Leftrightarrow4x+6=0\)

\(\Leftrightarrow2\left(2x+3\right)=0\)

\(\Leftrightarrow2x=-3\)

\(\Leftrightarrow x=\frac{-3}{2}\)

đề sai nhé

phải là

8. (x-1) . (x²+x+1)

\(pt\Leftrightarrow7\left(x+y\right)=3\left(x^2-xy+y^2\right)\)

\(\Leftrightarrow3x^2-\left(3y+7\right)x+3y^2-7y=0\)

\(\Delta\text{(}x\text{)}=\left(3y+7\right)^2-4.3\left(3y^2-7y\right)=...\)

Để x nguyên thì Delta phải là số chính phương.

-4 nha bạn !

\(ĐK:x\ge1\)

\(PT\Leftrightarrow x+3-4\sqrt{x+3}+4+\sqrt{x-1}=0\)

\(\Leftrightarrow\left(\sqrt{x+3}-2\right)^2+\sqrt{x-1}=0\)

\(\Leftrightarrow\hept{\begin{cases}\sqrt{x+3}=2\\x-1=0\end{cases}\Leftrightarrow}x=1\left(tm\right)\)

b) \(\frac{3\left(2x+1\right)}{4}-\frac{5x+3}{6}+\frac{x+1}{3}=\frac{x+7}{12}\)

<=> \(\frac{13\left(x+1\right)}{12}-\frac{5x+3}{6}=\frac{x+7}{12}\)

<=> 13(x + 1) - 2(5x + 3) = x + 7

<=> 13x + 13 - 10x - 6 = x + 7

<=> 3x + 7 = x + 7

<=> 3x + 7 - x = 7

<=> 2x + 7 = 7

<=> 2x = 7 - 7

<=> 2x = 0

<=> x = 0

c) 2x + 4(x - 2) = 5

<=> 2x + 4x - 8 = 5

<=> 6x - 8 = 5

<=> 6x = 5 + 8

<=> 6x = 13

<=> x = 13/6

Giải PT hay gì thế

\(\left(x+3\right)^2+\left(x-2\right)^2=2x^2+2x+13\)

\(\Leftrightarrow x^2+6x+9+x^2-4x+4=2x^2+2x+13\)

\(\Leftrightarrow2x^2+2x+13=2x^2+2x+13\) Luôn đúng với mọi x

 \(a)P=\left(\dfrac{x^2+2}{x^3-1}+\dfrac{x+1}{x^2+x+1}+\dfrac{1}{1-x}\right).\left(\dfrac{x^2}{x+1}+1\right).\left(x\ne1;x\ne-1\right).\\ P=\dfrac{x^2+2+x^2-1-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{x+1}.\\ P=\dfrac{x^2-x}{x-1}.\dfrac{1}{x+1}.\\ P=\dfrac{x\left(x-1\right)}{x-1}.\dfrac{1}{x+1}.\\ P=x.\dfrac{1}{x+1}.\\ P=\dfrac{x}{x+1}.\)

\(P=\dfrac{1}{4}.\Rightarrow\dfrac{x}{x+1}=\dfrac{1}{4}.\\ \Leftrightarrow4x-x-1=0.\\ \Leftrightarrow3x-1=0.\\ \Leftrightarrow x=\dfrac{1}{3}\left(TM\right).\)