\(ĐK:x\ge\dfrac{3}{2}\\ PT\Leftrightarrow3\sqrt{2x-3}-2\sqrt{2x-3}+6\sqrt{2x-3}=1\\ \Leftrightarrow7\sqrt{2x-3}=1\\ \Leftrightarrow\sqrt{2x-3}=\dfrac{1}{7}\\ \Leftrightarrow2x-3=\dfrac{1}{49}\Leftrightarrow x=\dfrac{74}{49}\left(tm\right)\)

\(x^4-16x^2+32x-16=0\)

\(\Leftrightarrow x^4-2x^3+2x^3-4x^2-12x^2+24x+8x-16=0\)

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

\(\Leftrightarrow\left(x-2\right)\left(x^3+2x^2-12x+8\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-2x^2+4x^2-8x^2-4x+8\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left[x^2\left(x-2\right)+4x\left(x-2\right)-4\left(x-2\right)\right]=0\)

\(\Leftrightarrow\left(x-2\right)^2\left(x^2+4x-4\right)=0\)

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

Vậy.............

\(x^4-16x^2+32x-16=0\)

\(\Leftrightarrow x^4-16\left(x^2-2x+1\right)=0\)

\(\Leftrightarrow x^4-16\left(x-1\right)^2=0\)

\(\Leftrightarrow x^4-\left(4\left(x-1\right)\right)^2=0\)

\(\Leftrightarrow\left(x^2-4\left(x-1\right)\right).\left(x^2+4\left(x-1\right)\right)=0\)

\(\Leftrightarrow\left(x^2-4x+4\right).\left(x^2+4x-4\right)=0\)

\(\Leftrightarrow\left(x-2\right)^2.\left(x^2+4x-4\right)=0\)

\(\Leftrightarrow\)\(\left(x-2\right)^2=0\) hoặc \(x^2+4x-4=0\)

1) \(\left(x-2\right)^2=0\Leftrightarrow x-2=0\Leftrightarrow x=2\)

\(2\)) \(x^2+4x-4=0\Leftrightarrow x^2+4x+4-8=0\)

\(\Leftrightarrow\left(x+2\right)^2=8\)

\(\Leftrightarrow x+2=\sqrt{8}\) hoặc \(x+2=-\sqrt{8}\)

\(\Leftrightarrow x=\sqrt{8}-2\) \(x=-\sqrt{8}-2\)

Vậy tập nghiệm của phương trình là \(S=\left\{2;\sqrt{8}-2;-\sqrt{8}-2\right\}\)

\(x^4-16x^2+32x-16=0\)

\(\Leftrightarrow\left(x^4-16\right)-\left(16x^2-32x\right)=0\)

\(\Leftrightarrow\left(x^2-4\right)\left(x^2+4\right)-16x\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x^2+4\right)-16x\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3+2x^2-12x+8\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3-2x^2+4x^2-8x^2-4x+8\right)=0\)

\(\Leftrightarrow\left(x-2\right)^2\left(x^2+4x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x^2+4x-4=0\end{matrix}\right.\)

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

Vậy x có tập \(n_o\) \(S=\left\{2;-2+2\sqrt{2};-2-2\sqrt{2}\right\}\)

x + 1 3 + 3 2 x + 1 4 = 2 x + 3 x + 1 6 + 7 + 12 x 12 ⇔ x + 1 3 + 6 x + 3 4 = 5 x + 3 6 + 7 + 12 x 12

⇔ 4(x + 1) + 3(6x + 3) = 2(5x + 3) + 7 + 12x

⇔ 4x + 4 + 18x + 9 = 10x + 6 + 7 + 12x

⇔ 4x + 18x – 10x – 12x = 6 + 7 – 4 – 9

⇔ 0x = 0

Phương trình có vô số nghiệm.

a: ĐKXĐ: x>=1/2

\(PT\Leftrightarrow2\sqrt{2x-1}-2\cdot3\sqrt{2x-1}+2\cdot4\sqrt{2x-1}=12\)

=>\(4\sqrt{2x-1}=12\)

=>\(\sqrt{2x-1}=3\)

=>2x-1=9

=>2x=10

=>x=5(nhận)

b: Sửa đề: \(\sqrt{9x^2-6x+1}=4\)

=>|3x-1|=4

=>3x-1=4 hoặc 3x-1=-4

=>3x=5 hoặc 3x=-3

=>x=-1 hoặc x=5/3

a,

ĐK : \(x\ge\frac{-15}{2}\)

Phương trình đã cho tương đương với

\(\sqrt{2x+15}=32x^2+32x-20\)

\(\Leftrightarrow2x+15=\left(32x^2+32x-20\right)^2\)\(\Leftrightarrow1024x^4+2048x^3-256x^2-1282x+385=0\)

Phương trình này có 2 nghiệm  là \(\orbr{\begin{cases}x=\frac{1}{2}\\x=\frac{-11}{8}\end{cases}}\) nên dễ dàng có được

⇔ ( 16x² + 14x − 11 ) ( 64x² + 72x − 35 ) = 0

Kết hợp với điều kiên bài toán ta có nghiệm của phương trình là \(x=\frac{1}{2};x=\frac{-9-\sqrt{221}}{16}\)

b,\(x^2=\sqrt{2-x}+2\)

ĐK \(x\le2\)

\(PT\Leftrightarrow\sqrt{2-x}=x^2-2\)

\(\Leftrightarrow2-x=\left(x^2-2\right)^2=x^4-4x^2+4\)

\(\Leftrightarrow x^4-4x^2+x+2=0\Leftrightarrow\left(x-1\right)\left(x^3+x^2-3x-2\right)=0\)

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

Vì\(x^2-x-1>0\)nên

\(\orbr{\begin{cases}x-1=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-2\end{cases}\left(Tm\right)}}\)

ĐKXĐ:\(x\ne\pm\dfrac{1}{2}\)

\(\dfrac{1+8x}{4+8x}-\dfrac{4x}{12x-6}+\dfrac{32x^2}{3\left(4-16x^2\right)}=0\)

\(\Leftrightarrow\dfrac{1+8x}{4\left(2x+1\right)}-\dfrac{4x}{6\left(2x-1\right)}+\dfrac{32x^2}{-6\cdot\left(2x-1\right)\left(2x+1\right)}=0\)

\(\Leftrightarrow\dfrac{6\cdot\left(1+8x\right)\left(2x-1\right)}{24\left(2x-1\right)\left(2x+1\right)}-\dfrac{4\cdot4x\left(2x+1\right)}{24\left(2x-1\right)\left(2x+1\right)}-\dfrac{32x^2\cdot4}{24\left(2x-1\right)\left(2x+1\right)}=0\)

\(\Leftrightarrow96x^2-36x-6-36x^2-16x-144x^2=0\)

\(\Leftrightarrow-84x^2-52x-6=0\)

\(\Leftrightarrow\Delta=688\)

\(\Leftrightarrow\left[{}\begin{matrix}x_1=\dfrac{52-\sqrt{688}}{-168}=\dfrac{-13+\sqrt{43}}{42}\\x_2=\dfrac{52+\sqrt{688}}{-168}=\dfrac{-13-\sqrt{43}}{43}\end{matrix}\right.\)

Vậy pt có 2 nghiệm phân biệt............

\(2x^3+3x^2-32x=48\)

\(2x^3+3x^2-32x-48=0\)

\(\left(2x^3+3x^2\right)-\left(32x+48\right)=0\)

\(x^2\left(2x+3\right)-16\left(2x+3\right)=0\)

\(\left(x^2-16\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x^2-16=0\\2x+3=0\end{cases}\Rightarrow\orbr{\begin{cases}\left(x+4\right)\left(x-4\right)=0\Leftrightarrow\orbr{\begin{cases}x=-4\\x=4\end{cases}}\\x=-\frac{3}{2}\end{cases}}}\)\(\left(x+4\right)\left(x-4\right)\left(2x+3\right)=0\)

\(\hept{\begin{cases}x+4=0\\x-4=0\\2x+3=0\end{cases}\Rightarrow\hept{\begin{cases}x=-4\\x=4\\x=-\frac{3}{2}\end{cases}}}\)

\(2x^3+3x^2-32x=48\)

\(\Leftrightarrow2x^3+3x^2-32x-48=0\)

\(\Leftrightarrow\left(2x^3-32x\right)+\left(3x^2-48\right)=0\)

\(\Leftrightarrow2x\left(x^2-16\right)+3\left(x^2-16\right)=0\)

\(\Leftrightarrow\left(x^2-16\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x+4\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-4=0;x+4=0\\2x+3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\pm4\\x=\frac{-3}{2}\end{cases}}\)

Vậy tập nghiệm của pt là S={4;-4;-3/2}

_Học tốt_

Ta có \(2x^3+3x^2-32x=48\)

\(\Leftrightarrow2x^3+3x^2-32x-48=0\)

\(\Leftrightarrow2x^2\left(x+\frac{3}{2}\right)-32\left(x+\frac{3}{2}\right)=0\)

\(\Leftrightarrow\left(x+\frac{3}{2}\right)\left(2x^2-32\right)=0\)

\(\Leftrightarrow\left(x+\frac{3}{2}\right)2\left(x^2-16\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{3}{2}=0\\x^2-16=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=\pm4\end{cases}}}\)

Vậy đccm