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bạn hãy nhân ở mẫu với biểu thức tương ướng để tạo ra biểu thức liên hợp , là HĐT số 3 ạ
\(a,\frac{2xy}{2\sqrt{x}+3\sqrt{y}}=\frac{2xy.\left(2\sqrt{x}-3\sqrt{y}\right)}{\left(2\sqrt{x}+3\sqrt{y}\right)\left(2\sqrt{x}-3\sqrt{y}\right)}=\frac{4x\sqrt{x}y-6xy\sqrt{y}}{2x-3y}\)
\(b,\frac{\sqrt{x}+\sqrt{y}}{2\sqrt{x}}=\frac{\left(\sqrt{x}+\sqrt{y}\right)\sqrt{x}}{2\sqrt{x}\sqrt{x}}=\frac{x+\sqrt{xy}}{2x}\)
\(c,\frac{2}{\sqrt{3}+1}=\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}=\frac{2.\left(\sqrt{3}-1\right)}{2}=\sqrt{3}-1\)
\(d,\frac{6}{2\sqrt{3}+\sqrt{2}}=\frac{6\left(2\sqrt{3}-\sqrt{2}\right)}{\left(2\sqrt{3}+\sqrt{2}\right)\left(2\sqrt{3}-\sqrt{2}\right)}=\frac{6\left(2\sqrt{3}-\sqrt{2}\right)}{10}=\frac{6\sqrt{3}-3\sqrt{2}}{5}\)
\(A=\dfrac{2}{2.\sqrt[3]{2}+2+\sqrt[3]{2^2}}=\dfrac{2}{\left(\sqrt[3]{2}\right)^2+2.\left(\sqrt[3]{2}\right)+\left(\sqrt{2}\right)^2}\)
\(A=\dfrac{2.\left(\sqrt[3]{2}\right)-\left(\sqrt{2}\right)}{\left(\sqrt[3]{2}\right)-\left(\sqrt{2}\right)\left[\left(\sqrt[3]{2}\right)^2+2.\left(\sqrt[3]{2}\right)+\left(\sqrt{2}\right)^2\right]}=\dfrac{2.\left(\sqrt[3]{2}\right)-\left(\sqrt{2}\right)}{\left(\sqrt[3]{2}\right)^3-\left(\sqrt{2}\right)^3}=\dfrac{2.\left(\sqrt[3]{2}\right)-\left(\sqrt{2}\right)}{2-2\sqrt{2}}\)
\(A=\dfrac{2\left[.\left(\sqrt[3]{2}\right)-\left(\sqrt{2}\right)\right].\left(1+\sqrt{2}\right)}{2\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}=\left(\sqrt{2}+1\right)\left(\sqrt{2}-\sqrt[3]{2}\right)\)
\(x=\frac{2}{2\sqrt[3]{2}+2+\sqrt[3]{4}}=\frac{2\left(\sqrt[3]{4}-\sqrt[3]{2}\right)}{\left(\sqrt[3]{4}-\sqrt[3]{2}\right)\left(\sqrt[3]{4^2}+\sqrt[3]{4}.\sqrt[3]{2}+\sqrt[3]{2^2}\right)}\)
\(=\frac{2\left(\sqrt[3]{4}-\sqrt[3]{2}\right)}{\left(\sqrt[3]{4}\right)^3-\left(\sqrt[3]{2}\right)^3}=\sqrt[3]{4}-\sqrt[3]{2}\)
\(y=\frac{6}{2\sqrt[3]{2}-2+\sqrt[3]{4}}=\frac{2\left(\sqrt[3]{4}+\sqrt[3]{2}\right)}{\left(\sqrt[3]{4}+\sqrt[3]{2}\right)\left(\sqrt[3]{4^2}-\sqrt[3]{4}.\sqrt[3]{2}+\sqrt[3]{2^2}\right)}\)
\(=\frac{6\left(\sqrt[3]{4}+\sqrt[3]{2}\right)}{\left(\sqrt[3]{4}\right)^3+\left(\sqrt[3]{2}\right)^3}=\sqrt[3]{4}+\sqrt[3]{2}\)
\(P=\frac{xy}{x+y}=\frac{\sqrt[3]{4^2}-\sqrt[3]{2^2}}{2\sqrt[3]{4}}=\frac{\sqrt[3]{4}-1}{2}\)