1> 3x(x-2)-2x(2x-1)=(1-x)(1+x)

⇔\(3x^2\)-6x-\(4x^2\)+2x=1-\(x^2\)

⇔-1\(x^2\) - 4x= 1- \(x^2\)

⇔ -1\(x^2\) -4x+ \(x^2\) = 1

⇔-4x=1

⇔ x = \(\dfrac{-1}{4}\)

\(a,4x^2-\left(3x+1\right)\left(2x-1\right)=2\left(x-3\right)^2\)

\(\Leftrightarrow4x^2-\left(6x^2-3x+2x-1\right)=2\left(x^2-6x+9\right)\)

\(\Leftrightarrow4x^2-6x^2+x+1-2x^2+12x-18=0\)

\(\Leftrightarrow-4x^2+13x-17=0\)

\(\Leftrightarrow-4\left(x^2-\dfrac{13}{4}x+\dfrac{169}{64}\right)-\dfrac{103}{16}=0\)

\(\Leftrightarrow-4\left(x-\dfrac{13}{8}\right)^2=\dfrac{103}{16}\)

\(\Leftrightarrow\left(x-\dfrac{13}{8}\right)^2=\dfrac{-103}{64}\Rightarrow\) pt vô nghiệm

\(b,\left(5x-1\right)\left(x+1\right)-\left(2x-1\right)\left(2x+1\right)=x.\left(x+1\right)\)\(\Leftrightarrow5x^2+5x-x-1-\left(4x^2-1\right)=x^2+x\)

\(\Leftrightarrow5x^2+5x-x-1-4x^2+1-x^2-x=0\) \(\Leftrightarrow3x=0\Rightarrow x=0\)

\(c,7x^2-\left(2x-3\right)^2=1+3\left(x+2\right)^2\)

\(\Leftrightarrow7x^2-\left(4x^2-12x+9\right)=1+3\left(x^2+4x+4\right)\)

\(\Leftrightarrow7x^2-4x^2+12x-9=1+3x^2+12x+12\)\(\Leftrightarrow7x^2-4x^2+12x-9-1-3x^2-12x-12=0\)\(\Leftrightarrow-22=0\) ( vô lí)

Vậy phương trình vô nghiệm

1) \(\left(x+1\right)^3-\left(x-1\right)^3=6.\left(x+2\right)^2-9\)

\(\Leftrightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)=6\left(x^2+4x+4\right)-9\)

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=6x^2+24x+24-9\)

\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2-24x-24+9=0\)

\(\Leftrightarrow-24x-13=0\Leftrightarrow-24x=13\Leftrightarrow x=\dfrac{-13}{24}\) vậy \(x=\dfrac{-13}{24}\)

2) \(\left(2x-1\right).\left(4x^2+2x+1\right)+\left(1-2x\right)^3=3.\left(2x+3\right)^2\)

\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3=3\left(.4x^2+12x+9\right)\)

\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3=12x^2+36x+27\)

\(\Leftrightarrow8x^3+4x^2+2x-4x^2-2x-1+1-6x+12x^2-8x^3-12x^2-36x-27=0\)

\(\Leftrightarrow-42x-27=0\Leftrightarrow-42x=27\Leftrightarrow x=\dfrac{-27}{42}\) vậy \(x=\dfrac{-27}{42}\)

a, \(\left(x+1\right)^3-\left(x-1\right)^3=6\left(x+2\right)^2-9\)

\(\Rightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)=6\left(x^2+4x+4\right)-9\)

\(\Rightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1=6x^2+24x+24-9\)

\(\Rightarrow6x^2+2-6x^2-24x=24-9\)

\(\Rightarrow-24x=15-2\Rightarrow-24x=13\Rightarrow x=-\dfrac{13}{24}\)

Câu b tương tự

Chúc bạn học tốt!!!

Như thế này bn thấy rõ k

1:  \(=8x^3+12x^2+6x+1-8x^3+12x^2-6x+1-2\left(4x+3\right)^2+8\left(x+3\right)^2\)

\(=24x^2+2-2\left(16x^2+24x+9\right)+8\left(x^2+6x+9\right)\)

\(=24x^2+2-32x^2-48x-18+8x^2+48x+72\)

=56

2: \(=\left(4x^2+4x+1\right)\left(x-1\right)-2\left(x^3-6x^2+12x-8\right)+x\left(3-2x\right)\left(3+x\right)-\left(3x-3\right)^2\)

\(=4x^3-3x-1-2x^3+12x^2-24x+16+x\left(9-3x-2x^2\right)-\left(3x-3\right)^2\)

\(=2x^3+12x^2-27x+15+9x-3x^2-2x^3-9x^2+18x-9\)

\(=6\)

\(a,\left(2x+1\right)^2-3x^2+4=\left(1-x\right)\left(1+x\right)\)

\(\Leftrightarrow4x^2+4x+1-3x^2+4=1-x^2\)

\(\Leftrightarrow4x^2+4x+1-3x^2+4-1+x^2=0\)

\(\Leftrightarrow2x^2+4x+4=0\)

\(\Leftrightarrow2\left(x^2+2x+1\right)+2=0\)

\(\Leftrightarrow2\left(x+1\right)^2=-2\)

\(\Leftrightarrow\left(x+1\right)^2=-1\Rightarrow\) pt vô nghiệm

\(b,\left(4x-3\right)\left(4x+3\right)-2\left(x+2\right)^2=14x^2\)

\(\Leftrightarrow16x^2-9-2\left(x^2+4x+4\right)-14x^2=0\)

\(\Leftrightarrow16x^2-9-2x^2-8x-8-14x^2=0\)

\(\Leftrightarrow-8x-17=0\)

\(\Leftrightarrow-8x=17\)

\(\Leftrightarrow x=\dfrac{-17}{8}\)

\(c,\left(2x-1\right)\left(x+1\right)-x^2+1=\dfrac{1}{2}\left(x-1\right)^2\)

\(\Leftrightarrow2x^2+2x-x-1-x^2+1=\dfrac{1}{2}\left(x^2-2x+1\right)\)

\(\Leftrightarrow2x^2+2x-x-1-x^2+1-\dfrac{1}{2}x^2+x-\dfrac{1}{2}=0\)\(\Leftrightarrow\dfrac{1}{2}x^2+2x-\dfrac{1}{2}=0\)

\(\Leftrightarrow\dfrac{1}{2}\left(x^2+4x+4\right)-\dfrac{5}{2}=0\)

\(\Leftrightarrow\dfrac{1}{2}\left(x+2\right)^2=\dfrac{5}{2}\)

\(\Rightarrow\left(x+2\right)^2=5\)

\(\Rightarrow\left[{}\begin{matrix}x+2=-\sqrt{5}\\x+2=\sqrt{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\sqrt{5}-2\\x=\sqrt{5}-2\end{matrix}\right.\)

a) \(\left(2x+1\right)^2-3x^2+4=\left(1-x\right)\left(1+x\right)\)

\(\Leftrightarrow4x^2+4x+1-3x^2+4=1-x^2\)

\(\Leftrightarrow4x^2+4x+1-3x^2+4-1+x^2=0\)

\(\Leftrightarrow2x^2+4x+4=0\Leftrightarrow\left(\sqrt{2}x\right)^2+2.\sqrt{2}.\sqrt{2}x+\left(\sqrt{2}\right)^2+2=0\) \(\Leftrightarrow\left(\sqrt{2}x+\sqrt{2}\right)^2+2=0\)

ta có : \(\left(\sqrt{2}x+\sqrt{2}\right)^2\ge0\Rightarrow\left(\sqrt{2}x+\sqrt{2}\right)^2+2\ge2>0\forall x\)

\(\Rightarrow\) phương trình vô nghiệm

vậy phương trình vô nghiệm

b) \(\left(4x-3\right)\left(4x+3\right)-2\left(x+2\right)^2=14x^2\)

\(\Leftrightarrow16x^2-9-2\left(x^2+4x+4\right)=14x^2\)

\(\Leftrightarrow16x^2-9-2x^2-8x-8=14x^2\)

\(\Leftrightarrow16x^2-9-2x^2-8x-8-14x^2=0\)

\(\Leftrightarrow-8x-17=0\Leftrightarrow-8x=17\Leftrightarrow x=\dfrac{-17}{8}\)

vậy \(x=\dfrac{-17}{8}\)

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

\(\Leftrightarrow2x^2+2x-x-1-x^2+1=\dfrac{1}{2}\left(x^2-2x+1\right)\)

\(\Leftrightarrow2x^2+2x-x-1-x^2+1=\dfrac{1}{2}x^2-x+\dfrac{1}{2}\)

\(\Leftrightarrow2x^2+2x-x-1-x^2+1-\dfrac{1}{2}x^2+x-\dfrac{1}{2}=0\)

\(\Leftrightarrow\dfrac{1}{2}x^2+2x-\dfrac{1}{2}=0\Leftrightarrow\left(\dfrac{\sqrt{2}}{2}x\right)^2+2.\sqrt{2}.\dfrac{\sqrt{2}}{2}x+\left(\sqrt{2}\right)^2-\dfrac{5}{2}=0\)

\(\Leftrightarrow\left(\dfrac{\sqrt{2}}{2}x+\sqrt{2}\right)^2-\dfrac{5}{2}=0\Leftrightarrow\left(\dfrac{\sqrt{2}}{2}x+\sqrt{2}\right)^2=\dfrac{5}{2}\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{\sqrt{2}}{2}x+\sqrt{2}=\sqrt{\dfrac{5}{2}}\\\dfrac{\sqrt{2}}{2}x+\sqrt{2}=-\sqrt{\dfrac{5}{2}}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{\sqrt{2}}{2}x=\sqrt{\dfrac{5}{2}}-\sqrt{2}=\dfrac{\sqrt{10}-2\sqrt{2}}{2}\\\dfrac{\sqrt{2}}{2}x=-\sqrt{\dfrac{5}{2}}-\sqrt{2}=-\dfrac{\sqrt{10}+2\sqrt{2}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-2+\sqrt{5}\\x=-2-\sqrt{5}\end{matrix}\right.\)

vậy \(x=-2+\sqrt{5};x=-2-\sqrt{5}\)

1: \(=x^3-6x^2+12x-8-8x^3-36x^2-54x-27+7\left(x-1\right)^3\)

\(=-7x^3-42x^2-42x-35+7x^3-21x^2+21x-7\)

\(=-63x^2-21x-42\)

2: \(=x^3+125-\left(x^3-8\right)=125+8=133\)

3: \(=8x^3-27-8x^3-12x^2-6x-1=-12x^2-6x-28\)

a)\((x^2- 4).(x^2 - 10) = 72 Đặt x^2 - 7 = a(1), ta có (a+3)(a-3)=72 a^2-9=72 a^2=81 a=+-9 xét 2 trường hợp a = 9 và -9 khi thay vào (1) ta có..... tự lm nốt nha \)

b) nhóm x+1 vs x+4 và x+2 vs x+3 ta sẽ có (x²+5x+4)(x²+5x+6)(x+5)=40

câu c dễ lắm... bạn có thể làm 2 cách 1 là xét 2 th khi vế trái bằng vế phải hay trái dấu vế phải

hoặc cách 2 đưa về hiệu 2 bình phương nhá.. cách này dễ hơn

Sửa đề: \(\left(2x^2+1\right)\left(3x^2-1\right)-\left(4x^2-3\right)\left(x^2+1\right)=x^2\left(2x^2+1\right)\)

\(\Leftrightarrow6x^4-2x^2+3x^2-1-\left(4x^4+4x^2-3x^2-3\right)=2x^4+x^2\)

\(\Leftrightarrow6x^4+x^2-1-4x^4-x^2+3-2x^4-x^2=0\)

\(\Leftrightarrow-x^2+2=0\)

hay \(x\in\left\{\sqrt{2};-\sqrt{2}\right\}\)