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1: Khi x=3-2 căn 2 thì \(A=\dfrac{\sqrt{2}-1+2}{\sqrt{2}-1}=\dfrac{\sqrt{2}+1}{\sqrt{2}-1}=3+2\sqrt{2}\)

2: \(B=\dfrac{x+\sqrt{x}+2+\sqrt{x}-2}{x-4}=\dfrac{x+2\sqrt{x}}{x-4}=\dfrac{\sqrt{x}}{\sqrt{x}-2}\)

3: \(P=A:B=\dfrac{\sqrt{x}+2}{\sqrt{x}}:\dfrac{\sqrt{x}}{\sqrt{x}-2}=\dfrac{x-4}{x}\)

\(x\cdot P< =10\sqrt{x}-29-\sqrt{x-25}\)

=>\(x-4< =10\sqrt{x}-29-\sqrt{x-25}\)

\(\Leftrightarrow x-4-10\sqrt{x}+29< =-\sqrt{x-25}\)

=>\(x-10\sqrt{x}+25< =-\sqrt{x-25}\)

=>(căn x-5)^2<=-căn x-25

=>x-25=0

=>x=25

1 C

2 A

3 C

4 B

5 D

b)\(3x\left(x+3y\right)-6xy\left(x+3y\right)\)

\(=\left(3x-6xy\right)\left(x+3y\right)\)

c)\(x\left(x+y\right)-5x-5y\)

\(=x\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x-5\right)\left(x+y\right)\)

Bài 1: 

b. \(3x\left(x+3y\right)-6xy\left(x+3y\right)\)

= (3x - 6xy)(x + 3y)

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

c. \(x\left(x+y\right)-5x-5y\)

= x(x + y) - 5(x + y)

= (x - 5)(x + y)

d. \(3\left(x-y\right)-5x\left(y-x\right)\)

= 3(x - y) + 5x(x - y)

= (3 + 5x)(x - y)

Bài 3:

a. x + 6x² = 0

<=> x(1 + 6x) = 0

<=> \(\left[{}\begin{matrix}x=0\\1+6x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-1}{6}\end{matrix}\right.\)

b. 2(x + 3) - x(x + 3) = 0

<=> (2 - x)(x + 3) = 0

<=> \(\left[{}\begin{matrix}2-x=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

c. 5x(x - 2) - (2 - x) = 0

<=> 5x(x - 2) + (x - 2) = 0

<=> (5x + 1)(x - 2) = 0

<=> \(\left[{}\begin{matrix}5x+1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=2\end{matrix}\right.\)

d. (x + 1) = (x + 1)²

<=> (x + 1) - (x + 1)² = 0

<=> (1 - x - 1)(x + 1) = 0

<=> -x(x + 1) = 0

<=> \(\left[{}\begin{matrix}-x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)