Rút gọn các biểu thức sau (giả thiết các biểu thức chữ đều có nghĩa):
a. \(\sqrt{18\left(\sqrt{2}-\sqrt{3}\right)^2};\)
b. \(ab\sqrt{1+\dfrac{1}{a^2b^2}};\)
c. \(\sqrt{\dfrac{a}{b^3}+\dfrac{a}{b^4}};\)
d. \(\dfrac{a+\sqrt{ab}}{\sqrt{a}+\sqrt{b}}.\)
a) ĐS:
.
b) ĐS: Nếu
thì ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?ab%5Csqrt%7B1+%5Cfrac%7B1%7D%7Ba%5E%7B2%7Db%5E%7B2%7D%7D%7D%3D%5Csqrt%7B%7Ba%5E%7B2%7Db%5E%7B2%7D+1%7D%7D.)
Nếu ab
c) ĐS:![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Csqrt%7Bab+a%7D%7D%7Bb%5E%7B2%7D%7D.)
d)![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7Ba+%5Csqrt%7Bab%7D%7D%7B%5Csqrt%7Ba%7D+%5Csqrt%7Bb%7D%7D%3D%5Cfrac%7B%28a+%5Csqrt%7Bab%7D%29%28%5Csqrt%7Ba%7D-%5Csqrt%7Bb%7D%29%7D%7Ba-b%7D%3D%5Cfrac%7Ba%5Csqrt%7Ba%7D-a%5Csqrt%7Bb%7D+%5Csqrt%7Bab%7D%5Csqrt%7Ba%7D-%5Csqrt%7Bab%7D%5Csqrt%7Bb%7D%7D%7Ba-b%7D)
Nhận xét. Nhận thấy rằng để
có nghĩa thì
Do đó
. Vì thế có thể phân tích tử thành nhân tử.
a) ĐS:
.
b) ĐS: Nếu
thì ![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?ab%5Csqrt%7B1+%5Cfrac%7B1%7D%7Ba%5E%7B2%7Db%5E%7B2%7D%7D%7D%3D%5Csqrt%7B%7Ba%5E%7B2%7Db%5E%7B2%7D+1%7D%7D.)
Nếu ab
c) ĐS:![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Csqrt%7Bab+a%7D%7D%7Bb%5E%7B2%7D%7D.)
d)![This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.](http://latex.codecogs.com/gif.latex?%5Cfrac%7Ba+%5Csqrt%7Bab%7D%7D%7B%5Csqrt%7Ba%7D+%5Csqrt%7Bb%7D%7D%3D%5Cfrac%7B%28a+%5Csqrt%7Bab%7D%29%28%5Csqrt%7Ba%7D-%5Csqrt%7Bb%7D%29%7D%7Ba-b%7D%3D%5Cfrac%7Ba%5Csqrt%7Ba%7D-a%5Csqrt%7Bb%7D+%5Csqrt%7Bab%7D%5Csqrt%7Ba%7D-%5Csqrt%7Bab%7D%5Csqrt%7Bb%7D%7D%7Ba-b%7D)
Nhận xét. Nhận thấy rằng để
có nghĩa thì
Do đó
. Vì thế có thể phân tích tử thành nhân tử.