Điều kiện xác định:

\(x\ge1\)

ta có: \(\left(\sqrt{5x-1}+\sqrt{x-1}\right)\left(3x-1-\sqrt{5x^2-6x+1}\right)=4x\)

\(\Leftrightarrow\)\(\left(\sqrt{5x-1}+\sqrt{x-1}\right)\left(\frac{5x-1+x-1}{2}-\sqrt{\left(5x-1\right)\left(x-1\right)}\right)=\left(5x-1\right)-\left(x-1\right)\)

Đặt \(\hept{\begin{cases}\sqrt{5x-1}=a\\\sqrt{x-1}=b\end{cases}}\)ta có \(\left(a+b\right)\left(\frac{a^2+b^2}{2}-ab\right)=a^2-b^2\)

\(\Leftrightarrow\frac{\left(a+b\right)\left(a-b\right)^2}{2}=\left(a-b\right)\left(a+b\right)\)

\(\Leftrightarrow\orbr{\begin{cases}\left(a-b\right)\left(a+b\right)=0\\a-b=2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}5x-1=x-1\\\sqrt{5x-1}-\sqrt{x-1}=2\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=0\\\sqrt{5x-1}=\sqrt{x-1}+2\end{cases}}\)

phương trình dưới ta bình phương hai vế được 

\(5x-1=x-1+4\sqrt{x-1}+4\Leftrightarrow4\left(x-1\right)=4\sqrt{x-1}\)

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

kết hợp điều kiện ta được hai nghiệm x=1 hoặc x=2

day ma la toan lop 1?

a, \(x^2-\frac{x^4}{x^2}-1=x^2-x^2-1=-1\)

b, \(\frac{x+9}{x^2-9}-\frac{3}{x^2+3x}=\frac{x+9}{\left(x-3\right)\left(x+3\right)}-\frac{3}{x\left(x+3\right)}\)

\(=\frac{x\left(x+9\right)}{x\left(x-3\right)\left(x+3\right)}-\frac{3\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}=\frac{x^2+9x-3x+9}{x\left(x-3\right)\left(x+3\right)}\)

\(=\frac{x^2+6x+9}{x\left(x-3\right)\left(x+3\right)}=\frac{\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}=\frac{x+3}{x\left(x-3\right)}\)

c, \(\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\frac{3x-2}{2x-4x^2}=\frac{1-3x}{2x}+\frac{3x-2}{2x-1}+\frac{3x-2}{2x\left(1-2x\right)}\)

\(=\frac{1-3x}{2x}-\frac{3x-2}{1-2x}+\frac{3x-2}{2x\left(1-2x\right)}=\frac{\left(1-3x\right)\left(1-2x\right)}{2x\left(1-2x\right)}-\frac{2x\left(3x-2\right)}{2x\left(1-2x\right)}+\frac{3x-2}{2x\left(1-2x\right)}\)

\(=\frac{1-2x-3x+6x^2-6x^2+4x+3x-2}{2x\left(1-2x\right)}=\frac{-1+2x}{2x\left(1-2x\right)}=\frac{-\left(1-2x\right)}{2x\left(1-2x\right)}=\frac{-1}{2x}\)

d, viết lại đề đy nhé 

e, \(\frac{x+1}{x-3}-\frac{1-x}{x+3}-\frac{2x\left(1-x\right)}{9-x^2}=\frac{x+1}{x-3}-\frac{1-x}{x+3}-\frac{2x-2x^2}{\left(3-x\right)\left(x+3\right)}\)

\(=\frac{x+1}{x-3}-\frac{1-x}{x+3}+\frac{2x-2x^2}{\left(x-3\right)\left(x+3\right)}=\frac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(1-x\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{2x-2x^2}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{x^2+3x+x+3-x+3+x^2+3x+2x-2x^2}{\left(x-3\right)\left(x+3\right)}=\frac{8x+6}{\left(x-3\right)\left(x+3\right)}\)

Xét tam giác ABH ta có : \(AB^2=BH^2+AH^2\Rightarrow15^2=12^2+AH^2\)

\(AH^2=AB^2-BH^2=15^2-12^2=81\Rightarrow AH=9\)cm 

Xét tam giác ACH ta có : \(AC^2=AH^2+HC^2\Rightarrow AC^2=AH^2+HC^2\)

\(HC^2=AC^2-AH^2=41^2-9^2=1600\Rightarrow HC=40\)cm 

Ta có : \(BC=CH+HB=40+12=52\)cm

\(\Rightarrow S_{ABC}=\frac{1}{2}AH.BC=\frac{1}{2}.9.52=234\)cm²