\(\Leftrightarrow\frac{5}{7}+\left|\frac{1}{2}-x\right|=\frac{11}{4}\)

\(\Leftrightarrow\left|\frac{1}{2}-x\right|=\frac{11}{4}-\frac{5}{7}=\frac{77-20}{28}=\frac{57}{28}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}-x=\frac{57}{28}\\\frac{1}{2}-x=-\frac{57}{28}\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}-\frac{57}{28}=\frac{14-57}{28}=\frac{-43}{28}\\x=\frac{1}{2}+\frac{57}{28}=\frac{14+57}{28}=\frac{71}{28}\end{cases}}\)

PT có 2 nghiệm là: -43/28 và 71/28

TH1 : \(x< \frac{1}{2}\), ta có:

\(-\frac{5}{7}-\left(\frac{1}{2}-x\right)=-\frac{11}{4}\)

\(-\frac{5}{7}-\frac{1}{2}+x=-\frac{11}{4}\)

\(-\frac{17}{14}+x=-\frac{11}{4}\)

\(x=-\frac{11}{4}-\left(-\frac{17}{14}\right)\)

\(x=-\frac{43}{28}\)( thỏa mãn )

TH2 : \(x\ge\frac{1}{2}\); ta có:

\(-\frac{5}{7}-\left(x-\frac{1}{2}\right)=-\frac{11}{4}\)

\(-\frac{5}{7}-x+\frac{1}{2}=-\frac{11}{4}\)

\(-\frac{3}{14}-x=-\frac{11}{4}\)

\(x=-\frac{3}{14}-\left(-\frac{11}{4}\right)\)

\(x=\frac{71}{28}\)(thỏa mãn)

Vậy \(\orbr{\begin{cases}x=\frac{-43}{28}\\x=\frac{71}{28}\end{cases}}\)

a: Ta có: \(2x\left(x-3\right)+x-3=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{1}{2}\end{matrix}\right.\)

b: Ta có: \(x^2\left(x-6\right)-x^2+36=0\)

\(\Leftrightarrow\left(x-6\right)\left(x^2-x-6\right)=0\)

\(\Leftrightarrow\left(x-6\right)\left(x-3\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=3\\x=-2\end{matrix}\right.\)

Bài 3:

a:

ĐKXĐ: x>=-5

\(x^2-7x=6\sqrt{x+5}-30\)

=>\(x^2-4x-3x+12=6\sqrt{x+5}-18\)

=>\(\left(x-4\right)\left(x-3\right)=6\left(\sqrt{x+5}-3\right)\)

=>\(\left(x-4\right)\left(x-3\right)=6\cdot\frac{x+5-9}{\sqrt{x+5}+3}\)

=>\(\left(x-4\right)\left(x-3-\frac{6}{\sqrt{x+5}+3}\right)=0\)

=>x-4=0

=>x=4(nhận)

Bài 2:

a: ĐKXĐ: x>=0

\(\sqrt{x+4\sqrt{x}+4}=5x+2\)

=>\(\sqrt{\left(\sqrt{x}+2\right)^2}=5x+2\)

=>\(5x+2=\sqrt{x}+2\)

=>\(5x-\sqrt{x}=0\)

=>\(\sqrt{x}\left(5\sqrt{x}-1\right)=0\)

=>\(\left[\begin{array}{l}\sqrt{x}=0\\ 5\sqrt{x}-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ \sqrt{x}=\frac15\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\left(nhận\right)\\ x=\frac{1}{25}\left(nhận\right)\end{array}\right.\)

b: \(\sqrt{x^2-2x+1}+\sqrt{x^2+4x+4}=4\)

=>\(\sqrt{\left(x-1\right)^2}+\sqrt{\left(x+2\right)^2}\) =4

=>|x-1|+|x+2|=4(1)

TH1: x<-2

(1) sẽ trở thành: -x-2+1-x=4

=>-2x-1=4

=>-2x=5

=>x=-5/2(nhận)

TH2: -2<=x<1

(1) sẽ trở thành: x+2+1-x=4

=>3=4(vô lý)

TH3: x>=1

(1) sẽ trở thành: x+2+x-1=4

=>2x+1=4

=>2x=3

=>x=3/2(nhận)

c: ĐKXĐ: x>=1

\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=2\)

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

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

=>\(\sqrt{x-1}+1+\left|\sqrt{x-1}-1\right|=2\)

=>\(\left|\sqrt{x-1}-1\right|=2-\sqrt{x-1}-1=1-\sqrt{x-1}\)

=>\(\sqrt{x-1}-1\le0\)

=>\(\sqrt{x-1}\le1\)

=>0<=x-1<=1

=>1<=x<=2

a. 6x² - (2x + 5)(3x - 2) = 7

<=> 6x² - 6x² + 4x - 15x + 10 = 7

<=> -11x = -3

<=> \(x=\dfrac{3}{11}\)

b. (5 - x)(25 + 5x + x²) + x(x² - 7) = 25

<=> 125 - x³ + x³ - 7x = 25

<=> -7x = 25 - 125

<=> -7x = -100

<=> \(x=\dfrac{100}{7}\)

c. (7 - 2x)² + (3 + 2x)(3 - 2x) = 30

<=> 49 - 28x + 4x² + 9 - 4x² = 30

<=> 4x² - 4x² - 28x = 30 - 49 - 9

<=> -28x = -28

<=> x = 1

Cảm ơn bạn rất nhiều ạ:3 <3

a: \(x^2-6x+5=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)

b: \(x\left(x+5\right)+x\left(x+15\right)=0\)

\(\Leftrightarrow x\left(2x+20\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)

\(-2,5\times\left(x+\dfrac{1}{5}\right)=\dfrac{7}{5}\)

\(\Leftrightarrow x+\dfrac{1}{5}=\dfrac{7}{5}:\left(-2,5\right)\)

\(\Leftrightarrow x+\dfrac{1}{5}=\dfrac{7}{5}\times\left(-\dfrac{2}{5}\right)\)

\(\Leftrightarrow x+\dfrac{1}{5}=-\dfrac{14}{25}\)

\(\Leftrightarrow x=-\dfrac{19}{25}\)

\(-2,5\cdot\left(x+\dfrac{1}{5}\right)=\dfrac{7}{5}\)

\(x+\dfrac{1}{5}=\dfrac{7}{5}:\left(-2,5\right)\)

\(x+\dfrac{1}{5}=\dfrac{7}{5}\times\left(-\dfrac{2}{5}\right)\)

\(x+\dfrac{1}{5}=-\dfrac{14}{25}\)

\(x=-\dfrac{14}{25}-\dfrac{1}{5}\)

\(x=-\dfrac{19}{25}\)

1+2+3+4+5+6+7+8+9=45

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = (9 + 1) + (8 + 2) + (7 + 3) + (6 + 4) + 5

= 10 + 10 + 10 + 10 + 5 = 45