m tự thêm kí hiệu nhé
P=\(\left(\sqrt{a}+2\right)\left(\sqrt{a}-3\right)=a-\sqrt{a}-6\)
P=\(\left(\sqrt{a}+1\right)^2=a+2\sqrt{a}+1\)
P=\(a-\sqrt{a}-6-\left(a+2\sqrt{a}+1\right)+3\sqrt{a}\)
P=-7
Tính :
a) \(\dfrac{5+2\sqrt{5}}{\sqrt{5}}+\dfrac{3+\sqrt{3}}{\sqrt{3}}-\left(\sqrt{5}+\sqrt{3}\right)\)
b) \(\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\right):\dfrac{1}{\sqrt{21+12\sqrt{3}}}\)
c) \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}\)
d) \(\sqrt{21-6\sqrt{6}}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
e) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
f) \(\dfrac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\left(\sqrt{5-2\sqrt{6}}\right)}{9\sqrt{3}-11\sqrt{2}}\)
g) \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)-\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}\)
V=\(\left(\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+1}\right)\left(\frac{x-1}{\sqrt{x}+1}-2\right)\)
W= \(\left(\frac{\sqrt{a}-1}{3\sqrt{a}+\left(\sqrt{a}-1\right)^2}-\frac{1-3\sqrt{a}+a}{a\sqrt{a}-1}-\frac{1}{\sqrt{a}-1}\right):\frac{a+1}{1-\sqrt{a}}\)
\(\dfrac{\left(a\sqrt{b}+b\right)\left(\sqrt{a}+\sqrt{b}\right)}{a-b}\sqrt{\dfrac{ab+b^2-2\sqrt{ab^3}3}{a\left(a+2\sqrt{b}\right)+b}}\)
Rút gọn các biểu thức:
1. A=\(\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)\)
2. B= \(\left(\sqrt{45}+\sqrt{63}\right)\left(\sqrt{7}-\sqrt{5}\right)\)
3. C= \(\left(\sqrt{5}+\sqrt{3}\right)\left(5-\sqrt{15}\right)\)
4. D= \(\left(\sqrt{32}-\sqrt{50}+\sqrt{27}\right)\left(\sqrt{27}+\sqrt{50}-\sqrt{32}\right)\)
5. E= \(\left(\sqrt{3}+1\right)^2-2\sqrt{3}+4\)
6. F= \(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
a) \(\sqrt{\left(2\sqrt{6}-4\right)^2}+\sqrt{15-6\sqrt{6}}\)
b) \(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{19+2\sqrt{18}}\)
c) \(\sqrt{9+4\sqrt{5}}-\sqrt{\left(1-\sqrt{5}^2\right)}\)
Bài 1:
a)\(\sqrt{\left(2\sqrt{6}-4\right)^2}+\sqrt{15-6\sqrt{6}}\)
b) \(\sqrt{\left(3-2\sqrt{2}\right)^2}+\sqrt{19+2\sqrt{18}}\)
c) \(\sqrt{9+4\sqrt{5}}-\sqrt{\left(1-\sqrt{5}^2\right)}\)
Bài 2: Biến đổi biểu thức
a) \(\dfrac{1}{\sqrt{7}+3}+\dfrac{1}{\sqrt{7}-3}\)
b) \(\dfrac{3}{\sqrt{2}-1}+\dfrac{\sqrt{6}+\sqrt{2}}{\sqrt{3}+1}\)
c) \(\dfrac{1}{7+4\sqrt{3}}+\dfrac{1}{7-4\sqrt{3}}\)
a.\(\sqrt{17}-6\sqrt{2}+3+\sqrt{2 }\)
b.\(\left(3+\sqrt{ }5\right).\left(\sqrt{ }10.\sqrt{ }2\right).\sqrt{3-\sqrt{ }5}\)
c.\(\left(\sqrt{2}-3\right).\sqrt{11+6\sqrt{2}}\)
d.\(\sqrt{23+8\sqrt{7}}-\sqrt{2}\)
nhanh nha gấp lắm trcs 9h
Khai triển và rút gọn biểu thức ( x ≥ 0, y ≥ 0 )
a, \(\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
b, \(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{x}\sqrt{y}+y\right)\)
c, \(\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)\)
Khai triển và rút gọn biểu thức (với x và y > 0):
a)\(\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
b)\(\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)\)
c)\(\left(2\sqrt{x}+\sqrt{y}\right)\left(3\sqrt{x}-2\sqrt{y}\right)\)
