x​ = 85. Nếu đúng thì k cho mình nha

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Bài tập 3:

\(S=\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\)

\(S^3=7+5\sqrt{2}+7-5\sqrt{2}+3\sqrt[3]{\left(7+5\sqrt{2}\right)\left(7-5\sqrt{2}\right)}.\left(\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\right)\)

( Áp dụng HĐT: \(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\)

\(S^3=14-3S\)

\(\Rightarrow S^3+3S-14=0\)

\(\Rightarrow S^3-2S^2+2S^2-4S+7S-14=0\)

\(\Rightarrow S^2\left(S-2\right)+2S\left(S-2\right)+7\left(S-2\right)=0\)

\(\Rightarrow\left(S-2\right)\left(S^2+2S+7\right)=0\)

\(\Rightarrow S-2=0\) ( Do: \(S^2+2S+7>0\))

\(\Rightarrow S=2\)

\(\dfrac{2\sqrt{X}-9}{x-5\sqrt{X}+6}-\dfrac{\sqrt{X}+3}{\sqrt{X}-2}-\dfrac{2\sqrt{X}+1}{3-\sqrt{X}}\) \(\left(X\ne2;X\ne3,X\ge0\right)\)

\(=\dfrac{2\sqrt{X}-9-\left(\sqrt{X}+3\right)\left(\sqrt{X}-3\right)+\left(2\sqrt{X}+1\right)\left(\sqrt{X}-2\right)}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}\)

\(=\dfrac{2\sqrt{X}-9-X+9+2X-4\sqrt{X}+\sqrt{X}-2}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}\)

\(=\dfrac{X-\sqrt{X}-2}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}=\dfrac{X-2\sqrt{X}+\sqrt{X}-2}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}\)

\(=\dfrac{\sqrt{X}\left(\sqrt{X}-2\right)+\left(\sqrt{X}-2\right)}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}=\dfrac{\left(\sqrt{X}-2\right)\left(\sqrt{X}+1\right)}{\left(\sqrt{X}-2\right)\left(\sqrt{X}-3\right)}=\dfrac{\sqrt{X}+1}{\sqrt{X}-3}\)

\(C=\dfrac{\sqrt{X}+1}{\sqrt{X}-3}< 1\)

\(\Rightarrow\dfrac{\sqrt{X}+1-\sqrt{X}+3}{\sqrt{X}-3}< 0\)

\(\Rightarrow\dfrac{4}{\sqrt{X}+3}< 0\) ( VÔ LÍ)

⇒ Không có X thỏa mãn