Tính
\(Q=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
NA
Những câu hỏi liên quan
tính:
P=\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Q=\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
1) \(P=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(4\sqrt{10}-4\sqrt{6}+\sqrt{150}-\sqrt{90}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{10}+\sqrt{6}\right)^2}\sqrt{4-\sqrt{15}}\)
\(=\sqrt{\left(\sqrt{10}+\sqrt{6}\right)^2+\left(4-\sqrt{15}\right)}\)
\(=\sqrt{\left(10+2\sqrt{60}+6\right)\cdot\left(4-\sqrt{15}\right)}\)
\(=\sqrt{\left(10+4\sqrt{15}+6\right)\cdot\left(4-\sqrt{15}\right)}\)
\(=\sqrt{\left(16+4\sqrt{15}\right)\cdot\left(4-\sqrt{15}\right)}\)
\(=\sqrt{4\left(4+\sqrt{15}\right)\cdot\left(4-\sqrt{15}\right)}\)
\(=\sqrt{4\left(16-15\right)}\)
\(=\sqrt{4\cdot1}\)
\(=\sqrt{4}\)
\(=2\)
2) \(Q=\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)
\(=\sqrt{\left(3-\sqrt{5}\right)^2}\sqrt{3+\sqrt{5}}+\sqrt{\left(3+\sqrt{5}\right)^2}\sqrt{3-\sqrt{5}}\)
\(=\sqrt{\left(3-\sqrt{5}\right)^2\cdot\left(3+\sqrt{5}\right)}+\sqrt{\left(3+\sqrt{5}\right)^2\cdot\left(3-\sqrt{5}\right)}\)
\(=\sqrt{\left(9-6\sqrt{5}+5\right)\cdot\left(3+\sqrt{5}\right)}+\sqrt{\left(9+6\sqrt{5}+5\right)\cdot\left(3-\sqrt{5}\right)}\)
\(=\sqrt{\left(14-6\sqrt{5}\right)\cdot\left(3+\sqrt{5}\right)}+\sqrt{\left(9+6\sqrt{5}+5\right)\cdot\left(3-\sqrt{5}\right)}\)
\(=\sqrt{42+14\sqrt{5}-18\sqrt{5}-30}+\sqrt{42-14\sqrt{5}+18\sqrt{5}-30}\)
\(=\sqrt{12-4\sqrt{5}}+\sqrt{12+4\sqrt{5}}\)
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\(\frac{\left(\sqrt{3-\sqrt{5}}-1\right)\left(\sqrt{3-\sqrt{5}}\left(3-\sqrt{5}\right)+1\right)}{4-\sqrt{5}-\sqrt{3-\sqrt{5}}}+\sqrt{5}\)\(\sqrt{5}\)
TÍNH BIỂU THỨC TRÊN
x^3left(sqrt[3]{5+2sqrt{6}}+sqrt[3]{5-2sqrt{6}}right)^3sqrt[3]{5+2sqrt{6}}^3+3sqrt[3]{left(5+2sqrt{6}right)^2}.sqrt[3]{5-2sqrt{6}}+3sqrt[3]{5+2sqrt{6}}.sqrt[3]{left(5-2sqrt{6}right)^2}+sqrt[3]{5-2sqrt{6}}^35+2sqrt{6}+3sqrt[3]{left(5+2sqrt{6}right)left(5-2sqrt{6}right)}.sqrt[3]{5+2sqrt{6}}+3sqrt[3]{left(5+2sqrt{6}right)left(5-2sqrt{6}right)}.sqrt[3]{5-2sqrt{6}}+5-2sqrt{6}5+5+3sqrt[3]{left(25-4.6right)}.sqrt[3]{5+2sqrt{6}}+3sqrt[3]{left(25-4.6right)}.sqrt[3]{5-2sqrt{6}}10+
3sqrt[3]{5+2sqrt{6}}+3sq...
Đọc tiếp
\(x^3=\left(\sqrt[3]{5+2\sqrt{6}}+\sqrt[3]{5-2\sqrt{6}}\right)^3=\sqrt[3]{5+2\sqrt{6}}^3\)
\(+3\sqrt[3]{\left(5+2\sqrt{6}\right)^2}.\sqrt[3]{5-2\sqrt{6}}+3\sqrt[3]{5+2\sqrt{6}}.\sqrt[3]{\left(5-2\sqrt{6}\right)^2}+\sqrt[3]{5-2\sqrt{6}}^3\)
\(=5+2\sqrt{6}+3\sqrt[3]{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}.\sqrt[3]{5+2\sqrt{6}}\)
\(+3\sqrt[3]{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}.\sqrt[3]{5-2\sqrt{6}}+5-2\sqrt{6}\)
\(=5+5+3\sqrt[3]{\left(25-4.6\right)}.\sqrt[3]{5+2\sqrt{6}}+3\sqrt[3]{\left(25-4.6\right)}.\sqrt[3]{5-2\sqrt{6}}\)
\(=10+ 3\sqrt[3]{5+2\sqrt{6}}+3\sqrt[3]{5-2\sqrt{6}}\)
p/s : có bạn hỏi nên mình đăng , các bạn đừng report nhé
Tính:
1.sqrt{left(sqrt{3}+sqrt{2}right)^2} 4.sqrt{left(sqrt{3}right)^2+2.left(sqrt{3}right).left(1right)+left(1right)^2}
2.sqrt{left(sqrt{5}-sqrt{6}right)^2} 5.sqrt{left(sqrt{5}right)^2+2.left(sqrt{5}right).left(sqrt{3}right)+left(sqrt{3}right)^2}
3.sqrt{left(2sqrt{2}+sqrt{3}right)^2}...
Đọc tiếp
Tính:
1.\(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\) 4.\(\sqrt{\left(\sqrt{3}\right)^2+2.\left(\sqrt{3}\right).\left(1\right)+\left(1\right)^2}\)
2.\(\sqrt{\left(\sqrt{5}-\sqrt{6}\right)^2}\) 5.\(\sqrt{\left(\sqrt{5}\right)^2+2.\left(\sqrt{5}\right).\left(\sqrt{3}\right)+\left(\sqrt{3}\right)^2}\)
3.\(\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}\) 6.\(\sqrt{\left(\sqrt{6}\right)^2-2.\left(\sqrt{6}\right).\left(\sqrt{5}\right)+\left(\sqrt{5}\right)^2}\)
Giup dum mik
Tính:
\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)\(\left(4+\sqrt{15}\right)\sqrt{4-\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)\)
\(\sqrt{3-\sqrt{5}}\sqrt{3-\sqrt{5}}\)\(\sqrt{3+\sqrt{5}}\)\(+\sqrt{3+\sqrt{5}}\sqrt{3+\sqrt{5}}\sqrt{3-\sqrt{5}}\)
=\(\sqrt{3-\sqrt{5}}\cdot\sqrt{3^2-5}+\sqrt{3+\sqrt{5}}\cdot\sqrt{3^2-5}\)=\(2\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)=\sqrt{2}\left(\sqrt{2\cdot3-2\sqrt{5}}+\sqrt{2\cdot3+2\sqrt{5}}\right)\) =\(=\sqrt{2}\left(\sqrt{5}-1+\sqrt{5}+1\right)=2\sqrt{10}\)
b tuong tu nha ban ^.^
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(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
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thực hiện phép tính :
G=\(\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)\left(-\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\)
mn ơi giúp mik vs ạ !!
\(\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\left(\sqrt{2}+\sqrt{3}-\sqrt{5}\right)\left(\sqrt{2}-\sqrt{3}+\sqrt{5}\right)\left(-\sqrt{2}+\sqrt{3}+\sqrt{5}\right)\)
\( \left( {\sqrt 2 + \sqrt 3 + \sqrt 5 } \right)\left( {\sqrt 2 + \sqrt 3 - \sqrt 5 } \right)\left( {\sqrt 2 - \sqrt 3 + \sqrt 5 } \right)\left( { - \sqrt 2 + \sqrt 3 + \sqrt 5 } \right)\\ = \left[ {{{\left( {\sqrt 2 + \sqrt 3 } \right)}^2} - 5} \right]\left( {\sqrt 5 + \sqrt 2 - \sqrt 3 } \right)\left( {\sqrt 5 - \sqrt 2 + \sqrt 3 } \right)\\ = \left( {2 + 2\sqrt 6 + 3 - 5} \right)\left[ {5 - {{\left( {\sqrt 2 - \sqrt 3 } \right)}^2}} \right]\\ = 2\sqrt 6 \left[ {5 - \left( {2 - 2\sqrt 6 + 3} \right)} \right]\\ = 2\sqrt 6 .2\sqrt 6 \\ = 4\sqrt {36} = 4.6 = 24 \)
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Bài này dễ thôi chỉ cần áp dụng (a+b)(a-b)=a2-b2
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Giải phương trình
\(\frac{3\left(x-\sqrt{3}\right)\left(x-\sqrt{5}\right)}{\left(1-\sqrt{3}\right)\left(1-\sqrt{5}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{5}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{5}\right)}+\frac{5\left(x-1\right)\left(x+\sqrt{3}\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=3x-2\)
left(sqrt{8-sqrt{X-3}}-sqrt{5-sqrt{X-3}}right)^25^25^2Leftrightarrow-2sqrt{left(8-sqrt{X-3}right)left(5-sqrt{X-3}right)}25-322Leftrightarrow-sqrt{left(8-sqrt{X-3}right)left(5-sqrt{X-3}right)}11Do sqrt{left(8-sqrt{X-3}right)left(5-sqrt{X-3}right)}ge0Rightarrow-sqrt{left(8-sqrt{X-3}right)left(5-sqrt{X-3}right)}le0RightarrowPT vô nghiệm
Đọc tiếp
\(\left(\sqrt{8-\sqrt{X-3}}-\sqrt{5-\sqrt{X-3}}\right)^2=5^2\)=\(5^2\)
\(\Leftrightarrow-2\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}=25-3=22\)
\(\Leftrightarrow-\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}=11\)
Do \(\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}\ge0\Rightarrow-\sqrt{\left(8-\sqrt{X-3}\right)\left(5-\sqrt{X-3}\right)}\le0\)
\(\Rightarrow\)PT vô nghiệm