\(\sqrt{\dfrac{a}{b}}\) +\(\dfrac{a}{b}\sqrt{\dfrac{a}{b}}\)
Những câu hỏi liên quan
1, Cho a, b, c là 3 số dương. CMR:
a, \(\dfrac{a}{\sqrt{a+b}\sqrt{a+c}}+\dfrac{b}{\sqrt{a+b}\sqrt{b+c}}+\dfrac{c}{\sqrt{a+c}\sqrt{b+c}}\le\dfrac{3}{2}\)
b, \(\dfrac{a}{\sqrt{a+b}\sqrt{b+c}}+\dfrac{b}{\sqrt{a+c}\sqrt{b+c}}+\dfrac{c}{\sqrt{a+c}\sqrt{b+a}}\ge\dfrac{3}{2}\)
Rut gon phuong trinh \(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a^6}+\sqrt{b^6}}{a-b}\)
A \(\dfrac{\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\)
B\(\dfrac{\sqrt{ab}-2b}{\sqrt{a}-\sqrt{b}}\)
C \(\dfrac{2b}{\sqrt{a}-\sqrt{b}}\)
D\(\dfrac{\sqrt{ab}-2a}{\sqrt{a}-\sqrt{b}}\)
Giup minh chon dap an dung
17 tháng 11 2021 lúc 9:22
với a > 0, b > 0 thì \(\sqrt{\dfrac{a}{b}}+\dfrac{a}{b}\sqrt{\dfrac{b}{a}}\)bằng:
a) 2
b) \(\dfrac{2\sqrt{ab}}{b}\)
c) \(\sqrt{\dfrac{a}{b}}\)
d) \(\sqrt{\dfrac{2a}{b}}\)
\(=\dfrac{\sqrt{ab}}{b}+\sqrt{\dfrac{a^2b}{b^2a}}=\dfrac{\sqrt{ab}}{b}+\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{ab}}{b}+\dfrac{\sqrt{ab}}{b}=\dfrac{2\sqrt{ab}}{b}\left(B\right)\)
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Thực hiện phép tính.
a) \(\left(\sqrt{ab}+2\sqrt{\dfrac{b}{a}}-\sqrt{\dfrac{a}{b}+\sqrt{\dfrac{1}{ab}}}\right)\sqrt{ab}\)
b) \(\left(\dfrac{am}{b}\sqrt{\dfrac{n}{m}}-\dfrac{ab}{n}\sqrt{mn}+\dfrac{a^2}{b^2}\sqrt{\dfrac{m}{n}}\right).a^2b^2.\sqrt{\dfrac{n}{m}}\)
Giải chi tiết ra hộ mình với ạ, mình cảm ơn ạ.
rút gọn pt
\(\left(\dfrac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\right)\sqrt{\dfrac{1}{b}-\dfrac{1}{a}}\)
\(=\dfrac{a+2\sqrt{ab}+b-a+2\sqrt{ab}-b}{a-b}\cdot\dfrac{\sqrt{ab}\cdot\sqrt{a-b}}{ab}\)
\(=\dfrac{4ab}{ab}\cdot\dfrac{1}{\sqrt{a-b}}=\dfrac{4}{\sqrt{a-b}}\)
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\(\dfrac{ab}{\sqrt{b}}-a\sqrt{\dfrac{b}{a}}+b\sqrt{\dfrac{a}{b}}-\dfrac{ab}{\sqrt{a}}\)
\(\dfrac{ab}{\sqrt{b}}-a\sqrt{\dfrac{b}{a}}+b\sqrt{\dfrac{a}{b}}-\dfrac{ab}{\sqrt{a}}\)
\(=a\sqrt{b}-\sqrt{ab}+\sqrt{ab}-b\sqrt{a}\)
\(=a\sqrt{b}-b\sqrt{a}\)
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\(\dfrac{ab}{\sqrt{b}}-a\sqrt{\dfrac{b}{a}}+b\sqrt{\dfrac{a}{b}}-\dfrac{ab}{\sqrt{a}}\)
\(\dfrac{ab}{\sqrt{b}}-a\sqrt{\dfrac{b}{a}}+b\sqrt{\dfrac{a}{b}}-\dfrac{ab}{\sqrt{a}}\\ =\dfrac{ab}{\sqrt{b}}-\dfrac{a\sqrt{b}}{\sqrt{a}}+\dfrac{b\sqrt{a}}{\sqrt{b}}-\dfrac{ab}{\sqrt{a}}\\ =\dfrac{ab+b\sqrt{a}}{\sqrt{b}}-\dfrac{a\sqrt{b}+ab}{\sqrt{a}}\\ =\dfrac{\sqrt{b}\left(a\sqrt{b}+\sqrt{ab}\right)}{\sqrt{b}}-\dfrac{\sqrt{a}\left(\sqrt{ab}+\sqrt{a}b\right)}{\sqrt{a}}\\ =a\sqrt{b}+\sqrt{ab}-\sqrt{ab}+\sqrt{a}b=a\sqrt{b}+b\sqrt{a}\)
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thực hiện phép tính ( rút gọn biểu thức )
a) \(\dfrac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}:\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\)
b) \(\dfrac{a-b}{\sqrt{a}+\sqrt{b}}-\dfrac{a-2\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
a: \(=\dfrac{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}}:\dfrac{1}{\sqrt{a}-\sqrt{b}}\)
\(=\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)=a-b\)
b: \(=\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}+\sqrt{b}}-\dfrac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}\)
\(=\sqrt{a}-\sqrt{b}-\sqrt{a}+\sqrt{b}\)
=0
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Chứng minh :
a) dfrac{3x}{2y}+dfrac{3}{2}sqrt{dfrac{3}{5}}-sqrt{dfrac{3}{4}}dfrac{3sqrt{x}}{2}.left(dfrac{sqrt{x}}{y}+sqrt{dfrac{3}{5x}}-sqrt{dfrac{1}{3}}right)
b)ab.sqrt{1+dfrac{1}{a^2b^2}}-sqrt{a^2b^2+1}0 , với a ; b 0
c) left(dfrac{3}{a}sqrt{dfrac{a^3}{b}}-dfrac{1}{2}sqrt{dfrac{4}{ab}}-2sqrt{dfrac{b}{a}}right):sqrt{dfrac{1}{ab}}3a-2b-1 với a, b 0
d)left(sqrt{dfrac{16a}{b}}+3sqrt{4ab}-asqrt{dfrac{36b}{a}}+2sqrt{ab}right):left(sqrt{ab}+dfrac{a}{b}sqrt{dfrac{b}{a}}+sqrt{dfrac{a}{b}}rig...
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Chứng minh :
a) \(\dfrac{3x}{2y}+\dfrac{3}{2}\sqrt{\dfrac{3}{5}}-\sqrt{\dfrac{3}{4}}=\dfrac{3\sqrt{x}}{2}.\left(\dfrac{\sqrt{x}}{y}+\sqrt{\dfrac{3}{5x}}-\sqrt{\dfrac{1}{3}}\right)\)
b)\(ab.\sqrt{1+\dfrac{1}{a^2b^2}}-\sqrt{a^2b^2+1}=0\) , với a ; b > 0
c) \(\left(\dfrac{3}{a}\sqrt{\dfrac{a^3}{b}}-\dfrac{1}{2}\sqrt{\dfrac{4}{ab}}-2\sqrt{\dfrac{b}{a}}\right):\sqrt{\dfrac{1}{ab}}=3a-2b-1\) với a, b >0
d)\(\left(\sqrt{\dfrac{16a}{b}}+3\sqrt{4ab}-a\sqrt{\dfrac{36b}{a}}+2\sqrt{ab}\right):\left(\sqrt{ab}+\dfrac{a}{b}\sqrt{\dfrac{b}{a}}+\sqrt{\dfrac{a}{b}}\right)=2\) Với a, b >0
Mọi người giúp tớ với ạ !!!!!! Mình thật sự cần gấp vào ngày mai !!!!
b)CM: \(ab\sqrt{1+\dfrac{1}{a^2b^2}}-\sqrt{a^2b^2+1}=0\)
\(VT=ab\sqrt{\dfrac{a^2b^2+1}{\left(ab\right)^2}}-\sqrt{a^2b^2+1}\)
\(VT=ab\dfrac{\sqrt{a^2b^2+1}}{ab}-\sqrt{a^2b^2+1}\)
\(VT=\sqrt{a^2b^2+1}-\sqrt{a^2b^2+1}\)
\(VT=0=VP\)
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Cho a, b là những số thực dương. Rút gọn các biểu thức sau:
a) dfrac{a^{dfrac{4}{3}}(a^{dfrac{-1}{3}}+a^{dfrac{2}{3}})}{a^{dfrac{1}{4}}(a^{dfrac{3}{4}}+a^{dfrac{-1}{4}})}
b) dfrac{b^{dfrac{1}{5}} (sqrt[5]{b^4}-sqrt[5]{b^{-1}})}{b^{dfrac{2}{3}}(sqrt[3]{b}-sqrt[3]{b^{-2}})}
c) dfrac{a^{dfrac{1}{3}}b^{dfrac{-1}{3}}-a^{dfrac{-1}{3}}b^{dfrac{1}{3}}}
{sqrt[3]{a^2}-sqrt[3]{b^2}}
d) dfrac{a^{dfrac{1}{3}} sqrt{b}+b^{dfrac{1}{3}} sqrt{a}}
{sqrt[6]{a}+sqrt[6]{b}}
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Cho a, b là những số thực dương. Rút gọn các biểu thức sau:
\(a)\ \dfrac{a^{\dfrac{4}{3}}(a^{\dfrac{-1}{3}}+a^{\dfrac{2}{3}})}{a^{\dfrac{1}{4}}(a^{\dfrac{3}{4}}+a^{\dfrac{-1}{4}})}\)
\(b)\ \dfrac{b^{\dfrac{1}{5}} (\sqrt[5]{b^4}-\sqrt[5]{b^{-1}})}{b^{\dfrac{2}{3}}(\sqrt[3]{b}-\sqrt[3]{b^{-2}})}\)
\(c)\ \dfrac{a^{\dfrac{1}{3}}b^{\dfrac{-1}{3}}-a^{\dfrac{-1}{3}}b^{\dfrac{1}{3}}}
{\sqrt[3]{a^2}-\sqrt[3]{b^2}}\)
\(d)\ \dfrac{a^{\dfrac{1}{3}} \sqrt{b}+b^{\dfrac{1}{3}} \sqrt{a}}
{\sqrt[6]{a}+\sqrt[6]{b}}\)
a) =
=
b) =
=
=
. ( Với điều kiện b # 1)
c) \(\dfrac{a^{\dfrac{1}{3}}b^{-\dfrac{1}{3}-}a^{-\dfrac{1}{3}}b^{\dfrac{1}{3}}}{\sqrt[3]{a^2}-\sqrt[3]{b^2}}\)= =
=
( với điều kiện a#b).
d) \(\dfrac{a^{\dfrac{1}{3}}\sqrt{b}+b^{\dfrac{1}{3}}\sqrt{a}}{\sqrt[6]{a}+\sqrt[6]{b}}\) = =
=
=
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