Viết dưới dạng latex để mik dễ hỗ trợ bn nhé

\(\sqrt{3x+15}=\sqrt{10} \)

\( \sqrt{4(1-x)^{2}}-6=0\)

a: ta có: \(\sqrt{3x+15}=\sqrt{10}\)

\(\Leftrightarrow3x+15=10\)

hay \(x=-\dfrac{5}{3}\)

Bài 1: 

b) \(\left(2x^2-3y\right)^3\)

\(=8x^6-3\cdot4x^4\cdot3y+3\cdot2x^2\cdot9y^2-27y^3\)

\(=8x^6-36x^4y+54x^2y^2-27y^3\)

Bạn nên đánh lại đề bài a nhé.

a,\(x\in\left\{5;1,5;\dfrac{-4}{3}\right\}\)

a: (x+2)(x-3)>0

nên x+2;x-3 cùng dấu

=>x>3 hoặc x<-2

b: (x-1)(x+4)<=0

nên x-1 và x+4 khác dấu

=>-4<=x<=1

a, \(2x\left(x-3\right)-15+5x=0\\ \Rightarrow2x\left(x-3\right)-\left(15-5x\right)=0\\ \Rightarrow2x\left(x-3\right)-5\left(3-x\right)=0\\ \Rightarrow\left(2x+5\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=3\end{matrix}\right.\)

b, \(x^3-7x=0\\ \Rightarrow x\left(x^2-7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=\pm7\end{matrix}\right.\)

c, \(\left(2x-3\right)^2-\left(x+5\right)^2=0\\ \Rightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\\ \Rightarrow\left(x-8\right)\left(3x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)

Xem lại đề câu d 

\(\left(3x-2\right)^2-6x+4=0\\ =>\left(3x-2\right)^2+2\left(-3x+2\right)=0\\ =>\left(2-3x\right)^2+2\left(2-3x\right)=0\\ =>\left(2-3x\right)\left(2-3x+2\right)=0\\ =>\left(2-3x\right)\left(4-3x\right)=0\\ \)

=> 2-3x=0 hoặc 4-3x=0

Nếu 2-3x=0 thì 3x=2 => \(x=\dfrac{2}{3}\)

Nếu 4-3x=0 thì 3x=4 => \(x=\dfrac{4}{3}\)

Vậy \(x=\dfrac{2}{3},x=\dfrac{4}{3}\)

b) (x+1)^3-x(x-2)^2+x-1=0

 ⇔x^3+3x^2+3x+1-(x^3-4x^2+4x)=0

⇔ x^3+3x^2+3x+1-x^3+4x^2-4x+x-1=0

⇔7x^2-2=0

⇔7x^2=2

⇔7x^2=-2⇔x=-3

⇔7x^2=2⇔x=-căn 5

a. \(x^2-25-3.\left(x-5\right)=0\\ \Leftrightarrow\left(x-5\right)\left(x+5\right)-3.\left(x-5\right)=0\\ \Leftrightarrow\left(x-5\right)\left(x+5-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

b. \(\left(3x+1\right)^2=\left(2x-5\right)\\ \Leftrightarrow9x^2+6x+1=2x-5\\ \Leftrightarrow9x^2+6x-2x=-5-1\\ \Leftrightarrow9x^2+4x=-6\\ \Leftrightarrow x\left(9x+4\right)=-6\\ \Leftrightarrow\left[{}\begin{matrix}x=-6\\9x+4=-6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=-\dfrac{10}{9}\end{matrix}\right.\)

c. \(2x^2-7x+6=0\\ \Leftrightarrow2x^2-7x=-6\\ \Leftrightarrow x\left(2x-7\right)=-6\\ \Leftrightarrow\left[{}\begin{matrix}x=-6\\x=\dfrac{1}{2}\end{matrix}\right.\)

a, \(\left(x-5\right)\left(x+5\right)-3\left(x-5\right)=0\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\Leftrightarrow x=-2;x=5\)

b, bạn ktra lại đề, thường thường ngta hay cho 2 vế cùng bình phương 

c, \(2x^2-7x+6=0\Leftrightarrow\left(2x-3\right)\left(x-2\right)=0\Leftrightarrow x=\dfrac{3}{2};x=2\)

\(\left(3x+1\right)^2=\left(2x-5\right)^2\)

\(\left[{}\begin{matrix}3x+1=2x-5\\3x+1=5-2x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\5x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=\dfrac{4}{5}\end{matrix}\right.\)