\(\hept{\begin{cases}\left(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}\right)^2=9\left(\sqrt[3]{5}-\sqrt[3]{4}\right)\\\left(3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\right)^2=9\left(\sqrt[3]{5}-\sqrt[3]{4}\right)\end{cases}}\)
Chứng tỏ: \(\sqrt[3]{20}+\sqrt[3]{2}-\sqrt[3]{25}=3\sqrt[3]{\sqrt[3]{5}-\sqrt[3]{4}}\)
Chứng minh \(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}\)= \(3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\)
Giúp mình với nha!!!!!! Mình sẽ tick cho các bạn
chứng minh các đẳng thức sau
a) \(\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}=1\)
b) \(\sqrt[3]{20+14\sqrt{2}}-\sqrt[3]{14\sqrt{2}-20}=4\)
\(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}=2\)
Rút gọn biểu thức
I=(2\(\sqrt{3}\)-5\(\sqrt{27}\)+4\(\sqrt{12}\)):\(\sqrt{3}\)
K=\(\sqrt{125}\)-4\(\sqrt{45}\)+3\(\sqrt{20}\)-\(\sqrt{80}\)
L=2\(\sqrt{9}\)+\(\sqrt{25}\)-5\(\sqrt{4}\)
N=2\(\sqrt{32}\)-5\(\sqrt{27}\)-4\(\sqrt{8}\)+3\(\sqrt{75}\)
O=2\(\sqrt{3.5^2}\)-3\(\sqrt{3.2^2}\)+\(\sqrt{3.3^2}\)
Chứng minh rằng:
a)\(\left(\sqrt[3]{3+2\sqrt{2}}+\sqrt[3]{3-2\sqrt{2}}\right)^8>3^6\)
b) \(\sqrt[3]{\sqrt[5]{\frac{32}{5}}-\sqrt[5]{\frac{27}{5}}}=\sqrt[5]{\frac{1}{25}}+\sqrt[5]{\frac{3}{25}}-\sqrt[5]{\frac{9}{25}}\)
Chứng minh đẳng thức sau:
\(\frac{a+\sqrt{2+\sqrt{5}}.\sqrt{\sqrt{9-4\sqrt{5}}}}{\sqrt[3]{2-\sqrt{5}}.\sqrt[3]{\sqrt{9+4\sqrt{5}}-\sqrt[3]{a^2}}+\sqrt[3]{a}}=-\sqrt[3]{a-1}\)
Chứng minh bất đẳng thức sau:
\(\left(\sqrt[3]{\sqrt{9+4\sqrt{5}}+\sqrt[3]{2+\sqrt{5}}}\right).\sqrt[3]{\sqrt{5-2}}-2,1< 0\)
cmr các đẳng thức :
1/\(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}=3\sqrt{\sqrt[3]{5}-\sqrt[3]{4}}\)
2/\(\frac{\sqrt[4]{5}+1}{\sqrt[4]{5}-1}=\sqrt[4]{\frac{3+2\sqrt[4]{5}}{3-2\sqrt[4]{5}}}\)
3/\(\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{\frac{1}{9}}-\sqrt[3]{\frac{2}{9}}+\sqrt[3]{\frac{4}{9}}\)
giúp mik vs mik cần gấp lắm
Tính:
a/ \(\frac{3+\sqrt{5}}{\sqrt{2}+\sqrt{3+\sqrt{5}}}+\frac{3-\sqrt{5}}{\sqrt{2}-\sqrt{3-\sqrt{5}}}\)
b/ \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}-\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\$\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
a \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
b \(\sqrt{x-1}+\sqrt{4x-4}-\sqrt{25x-25}=4\)
c \(\dfrac{1}{3}\sqrt{x-2}-\dfrac{2}{3}\sqrt{9x-18}+6\sqrt{\dfrac{x-2}{81}=-4}\)
d \(\sqrt{9x+27}+4\sqrt{x+3}-\dfrac{3}{4}\sqrt{16x+48}=0\)
