Lời giải:

$x-2\sqrt{x}-15=(x-5\sqrt{x})+(3\sqrt{x}-15)$

$=\sqrt{x}(\sqrt{x}-5)+3(\sqrt{x}-5)=(\sqrt{x}-5)(\sqrt{x}+3)$

\(\text{ x - 2 √ x - 15}\)

\(=x+3\sqrt{x}\)\(-5\sqrt{x}\)\(-15\)

\(=\left(x+3\sqrt{x}\right)\)\(-\left(5\sqrt{x}\right)\)\(+15\)

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

\(\left(\sqrt{x}+3\right)-5\left(\sqrt{x}-5\right)\)

Bài 2: 

a: Ta có: \(\sqrt{\sqrt{5}-x\sqrt{3}}=\sqrt{8+2\sqrt{15}}\)

\(\Leftrightarrow\sqrt{5}-x\sqrt{3}=8+2\sqrt{15}\)

\(\Leftrightarrow x\sqrt{3}=\sqrt{5}-8-2\sqrt{15}\)

\(\Leftrightarrow x=\dfrac{\sqrt{15}-8\sqrt{3}-6\sqrt{5}}{3}\)

b: Ta có: \(\sqrt{2+\sqrt{\sqrt{x}+3}}=3\)

\(\Leftrightarrow\sqrt{\sqrt{x}+3}=7\)

\(\Leftrightarrow\sqrt{x}=46\)

hay x=2116

1. $x+\sqrt{x}=\sqrt{x}(\sqrt{x}+1)$

2. $x-\sqrt{x}=\sqrt{x}(\sqrt{x}-1)$

3. $a+3\sqrt{a}-10=(a-2\sqrt{a})+(5\sqrt{a}-10)$

$=\sqrt{a}(\sqrt{a}-2)+5(\sqrt{a}-2)=(\sqrt{a}+5)(\sqrt{a}-2)$

4. $x\sqrt{x}+\sqrt{x}-x-1=(x\sqrt{x}+\sqrt{x})-(x+1)=\sqrt{x}(x+1)-(x+1)$

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

5. $x+\sqrt{x}-2=(x-\sqrt{x})+(2\sqrt{x}-2)$

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

6. $x-5\sqrt{x}+6=(x-2\sqrt{x})-(3\sqrt{x}-6)=\sqrt{x}(\sqrt{x}-2)-3(\sqrt{x}-2)=(\sqrt{x}-2)(\sqrt{x}-3)$

7. $x\sqrt{x}-1=(\sqrt{x})^3-1^3=(\sqrt{x}-1)(x+\sqrt{x}+1)$

8. $x\sqrt{x}-x+\sqrt{x}-1=x(\sqrt{x}-1)+(\sqrt{x}-1)=(\sqrt{x}-1)(x+1)$

9. $x+2\sqrt{x}-15=(x-3\sqrt{x})+(5\sqrt{x}-15)=\sqrt{x}(\sqrt{x}-3)+5(\sqrt{x}-3)=(\sqrt{x}-3)(\sqrt{x}+5)$

10. $x-2\sqrt{x}-3=(x+\sqrt{x})-(3\sqrt{x}+3)=\sqrt{x}(\sqrt{x}+1)-3(\sqrt{x}+1)=(\sqrt{x}+1)(\sqrt{x}-3)$

\(x+\sqrt{x}=\sqrt{x}\left(\sqrt{x}+1\right)\\ x-\sqrt{x}=\sqrt{x}\left(\sqrt{x}-1\right)\\ a+3\sqrt{a}-10=a+5\sqrt{a}-2\sqrt{a}-10=\sqrt{a}\left(\sqrt{a}+5\right)-2\left(\sqrt{a}+5\right)=\left(\sqrt{a}-2\right)\left(\sqrt{a}+5\right)\)

\(x\sqrt{x}+\sqrt{x}-x-1=\left(x\sqrt{x}-x\right)+\left(\sqrt{x}-1\right)=x\left(\sqrt{x}-1\right)+\sqrt{x}-1=\left(\sqrt{x}-1\right)\left(x+1\right)\\ x+\sqrt{x}-2=x+2\sqrt{x}-\sqrt{x}-2=\sqrt{x}\left(\sqrt{x}+2\right)-\left(\sqrt{x}+2\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\\ x-5\sqrt{x}+6=x-2\sqrt{x}-3\sqrt{x}-6=\sqrt{x}\left(\sqrt{x}-2\right)-3\left(\sqrt{x}-2\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)\)

Mấy bạn còn lại tương tự những bài trên nhé. Nếu còn thắc mắc ở chỗ nào bạn có thể liên hệ mình nhé. Nhớ lần sau bạn tách ra nha, chứ nhiều câu quá.

\(\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)

\(\left(\sqrt{x}-\sqrt{y}\right)^2\)

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

\(\left(\sqrt{15}x-4\right)^2\)

\(a\sqrt{a}-b\sqrt{b}\)

\(=\sqrt{a^3}-\sqrt{b^3}\)

\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)\)

\(x+y-2\sqrt{xy}\)

\(=\left(\sqrt{x}-\sqrt{y}\right)^2\)

a)  \(1+\sqrt{3}+\sqrt{5}+\sqrt{15}\)

\(=\left(1+\sqrt{3}\right)+\sqrt{5}\left(1+\sqrt{3}\right)\)

\(=\left(1+\sqrt{3}\right)\left(1+\sqrt{5}\right)\)

b)  \(\sqrt{10}+\sqrt{14}+\sqrt{15}+\sqrt{21}\)

\(=\sqrt{5}\left(\sqrt{2}+\sqrt{3}\right)+\sqrt{7}\left(\sqrt{2}+\sqrt{3}\right)\)

\(=\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{5}+\sqrt{7}\right)\)

c)  \(\sqrt{35}-\sqrt{15}+\sqrt{14}-\sqrt{6}\)

\(=\sqrt{5}\left(\sqrt{7}-\sqrt{3}\right)+\sqrt{2}\left(\sqrt{7}-\sqrt{3}\right)\)

\(=\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{2}\right)\)

e)  \(xy+y\sqrt{x}+\sqrt{x}+1\)

\(=y\sqrt{x}\left(\sqrt{x}+1\right)+\left(\sqrt{x}+1\right)\)

\(=\left(\sqrt{x}+1\right)\left(y\sqrt{x}+1\right)\)

g)  \(3+\sqrt{x}+9-x\)

\(=\left(3+\sqrt{x}\right)+\left(3+\sqrt{x}\right)\left(3-\sqrt{x}\right)\)

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

a) \(x-4\sqrt{x-2}+2\left(x\ge2\right)\) 

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

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

\(=\left(\sqrt{x-2}\right)^2-2\cdot2\cdot\sqrt{x-2}+2^2\)

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

b) \(x+4\sqrt{x-2}+2\left(x\ge2\right)\)

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

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

\(=\left(\sqrt{x-2}\right)^2+2\cdot2\cdot\sqrt{x-2}+2^2\)

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

\(x\sqrt{x}+2x+\sqrt{x}+2\left(x>0\right)\)

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

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

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

a) \(x\sqrt{x}+\sqrt{x}-x-1\) 

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

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

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

b) \(\sqrt{ab}+2\sqrt{a}+3\sqrt{b}+6\)

\(=\sqrt{a}\left(\sqrt{b}+2\right)+3\left(\sqrt{b}+2\right)\)

\(=\left(\sqrt{b}+2\right)\left(\sqrt{a}+3\right)\)

1)  \(x+5\sqrt{x}+6=x+2\sqrt{x}+3\sqrt{x}+6\)

                                 \(=\sqrt{x}\left(\sqrt{x}+2\right)+3\left(\sqrt{x}+2\right)\)

                                  \(=\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)\)

2)       \(=\left(4\sqrt{3}+3\sqrt{15}-12\sqrt{15}\right)\sqrt{3}\)

           \(=\left(4\sqrt{3}-8\sqrt{15}\right)\sqrt{3}=12-24\sqrt{5}\)