chứng minh rằng A = căn bậc 3 5 căn 2+7 -căn bậc 3 5 căn 2 -7 =2
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H9
HT.Phong (9A5)
CTVHS
23 tháng 8 2023
a) \(15\sqrt{\dfrac{4}{3}}-5\sqrt{48}+2\sqrt{12}-6\sqrt{\dfrac{1}{3}}\)
\(=\sqrt{15^2\cdot\dfrac{4}{3}}-5\cdot4\sqrt{3}+2\cdot2\sqrt{3}-\sqrt{6^2\cdot\dfrac{1}{3}}\)
\(=\sqrt{\dfrac{225\cdot4}{3}}-20\sqrt{3}+4\sqrt{3}-\sqrt{\dfrac{36}{3}}\)
\(=\sqrt{75\cdot4}-16\sqrt{3}-\sqrt{12}\)
\(=10\sqrt{3}-16\sqrt{3}-2\sqrt{3}\)
\(=-8\sqrt{3}\)
b) \(\dfrac{15}{\sqrt{6}+1}-\dfrac{3}{\sqrt{7}-\sqrt{2}}-15\sqrt{6}+3\sqrt{7}\)
\(=\dfrac{15\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}-\dfrac{3\left(\sqrt{7}+\sqrt{2}\right)}{\left(\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+\sqrt{2}\right)}-15\sqrt{6}+3\sqrt{7}\)
\(=\dfrac{15\left(\sqrt{6}-1\right)}{6-1}-\dfrac{3\sqrt{7}+3\sqrt{2}}{7-2}-15\sqrt{6}+3\sqrt{7}\)
\(=3\left(\sqrt{6}-1\right)-\dfrac{3\sqrt{7}+3\sqrt{2}}{5}-15\sqrt{6}+3\sqrt{7}\)
\(=3\sqrt{6}-3-\dfrac{3\sqrt{7}+3\sqrt{2}}{5}-15\sqrt{6}+3\sqrt{7}\)
\(=-12\sqrt{6}-3+3\sqrt{7}-\dfrac{3\sqrt{7}+3\sqrt{2}}{5}\)
\(=\dfrac{-60\sqrt{6}-15+15\sqrt{7}-3\sqrt{7}-3\sqrt{2}}{5}\)
\(=\dfrac{-60\sqrt{6}-15+12\sqrt{7}-3\sqrt{2}}{5}\)
VH
1
H9
HT.Phong (9A5)
CTVHS
24 tháng 10 2023
\(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\left(x\ge0\right)\)
\(=3\sqrt{2x}-5\sqrt{2^2\cdot2x}+7\sqrt{3^2\cdot2x}\)
\(=3\sqrt{2x}-5\cdot2\sqrt{2x}+7\cdot3\sqrt{2x}\)
\(=3\sqrt{2x}-10\sqrt{2x}+21\sqrt{2x}\)
\(=\left(3-10+21\right)\sqrt{2x}\)
\(=14\sqrt{2x}\)
NN
1
Ta có: \(A=\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\)
\(\Rightarrow A^3=5\sqrt{2}+7-5\sqrt{2}+7-3\left(5\sqrt{2}+7\right)\left(5\sqrt{2}-7\right)\left(\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}\right)\)
\(=14-3\left(50-49\right)A\)
\(\Rightarrow A^3=14-3A\Leftrightarrow A^3+3A-14=0=\left(A-2\right)\left(A^2+2A+7\right)=0\)
\(\Leftrightarrow A-2=0\Leftrightarrow A=2\)
=> Đpcm