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a,\(5+\sqrt{24}=5+\sqrt{6.4}=5+2\sqrt{6}=\left(\sqrt{2}\right)^2+2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^2=\left(\sqrt{2}+\sqrt{3}\right)^2\)
b,\(14+6\sqrt{5}=14+2.3.\sqrt{5}=3^2+2.3\sqrt{5}+\left(\sqrt{5}\right)^2=\left(3+\sqrt{5}\right)^2\)
`12+2sqrt35=7+2sqrt{7.5}+5=(sqrt7+sqrt5)^2`
`9+4sqrt2=8+2.2sqrt2+1=(2sqrt2+1)^2`
`9-4sqrt2=8-2.2sqrt2+1=(2sqrt2-1)^2`
\(12+2\sqrt{35}=\left(\sqrt{7}+\sqrt{5}\right)^2\)
\(9+4\sqrt{2}=\left(2\sqrt{2}+1\right)^2\)
\(9-4\left(\sqrt{2}\right)=\left(2\sqrt{2}-1\right)^2\)
\(11-6\sqrt{2}=\left(3-\sqrt{2}\right)^2\)
\(6+4\sqrt{2}=\left(2+\sqrt{2}\right)^2\)
Phiền ad có thể trình bày đầy đủ hộ em đc ko ạ? Vì em mới học sáng nay nên trình bày tắt thì em ko hiểu lắm. Em cảm ơn ạ :>
1) \(2x+5\sqrt{x}-7=2\left[\left(x+\dfrac{5}{2}\sqrt{x}+\dfrac{25}{16}\right)-\dfrac{25}{16}-\dfrac{7}{2}\right]\)
\(=2\left[\left(\sqrt{x}+\dfrac{5}{4}\right)^2-\dfrac{81}{16}\right]=2\left(\sqrt{x}+\dfrac{5}{4}-\dfrac{9}{4}\right)\left(\sqrt{x}+\dfrac{5}{4}+\dfrac{9}{4}\right)=2\left(\sqrt{x}-1\right)\left(\sqrt{x}+\dfrac{7}{2}\right)\)
2) \(3x-7\sqrt{x}+4=3\left[\left(x-\dfrac{7}{3}\sqrt{x}+\dfrac{49}{36}\right)-\dfrac{49}{36}+\dfrac{4}{3}\right]\)
\(=3\left[\left(\sqrt{x}-\dfrac{7}{6}\right)^2-\dfrac{1}{36}\right]=3\left(\sqrt{x}-\dfrac{7}{6}-\dfrac{1}{6}\right)\left(\sqrt{x}-\dfrac{7}{6}+\dfrac{1}{6}\right)=3\left(\sqrt{x}-\dfrac{4}{3}\right)\left(\sqrt{x}-1\right)\)
3) \(4x-4\sqrt{x}-8=4\left[\left(x-\sqrt{x}+\dfrac{1}{4}\right)-\dfrac{1}{4}-2\right]\)
\(=4\left[\left(\sqrt{x}-\dfrac{1}{2}\right)^2-\dfrac{9}{4}\right]=4\left(\sqrt{x}-\dfrac{1}{2}-\dfrac{3}{2}\right)\left(\sqrt{x}-\dfrac{1}{2}+\dfrac{3}{2}\right)=4\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\)
| \(2x+5\sqrt{x}-7=\left(\sqrt{x}-1\right)\left(2\sqrt{x}+7\right)\) |
| \(3x-7\sqrt{x}+4=\left(3\sqrt{x}-4\right)\left(\sqrt{x}-1\right)\) |
| \(4x-4\sqrt{x}-8=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\) |
`11+4sqrt6=8+2.2sqrt2.sqrt3+3=(2sqrt2+sqrt3)^2`
`11-4sqrt6=8-2.2sqrt2.sqrt3+3=(2sqrt2-sqrt3)^2`
`13+4sqrt10=8+2.2sqrt2.sqrt5+5=(2sqrt2+sqrt5)^2`
`13-4sqrt10=8-2.2sqrt2.sqrt5+5=(2sqrt2-sqrt5)^2`
Bạn vào link này:
Câu hỏi của Mai Ngô - Toán lớp 9 | Học trực tuyến
Câu a ta có phương trình:
\(t^2-9t+\frac{36.2}{4}=0\Rightarrow\left[{}\begin{matrix}t_1=6\\t_2=3\end{matrix}\right.\)
\(\Rightarrow9+6\sqrt{2}=\left(\sqrt{6}+\sqrt{3}\right)^2\)
Câu b ta có pt:
\(t^2-5t+\frac{4.6}{4}\Rightarrow\left[{}\begin{matrix}t_1=3\\t_2=2\end{matrix}\right.\)
\(\Rightarrow5-2\sqrt{6}=\left(\sqrt{3}-\sqrt{2}\right)^2\)
\(P=\dfrac{x+\sqrt{x}}{3\sqrt{x}-1}=\dfrac{7-4\sqrt{3}+\sqrt{7-4\sqrt{3}}}{3\sqrt{7-4\sqrt{3}}-1}=\dfrac{7-4\sqrt{3}+\sqrt{\left(2-\sqrt{3}\right)^2}}{3\sqrt{\left(2-\sqrt{3}\right)^2}-1}=\dfrac{7-4\sqrt{3}+\left|2-\sqrt{3}\right|}{3\left|2-\sqrt{3}\right|-1}=\dfrac{7-4\sqrt{3}+2-\sqrt{3}}{3\left(2-\sqrt{3}\right)-1}=\dfrac{9-5\sqrt{3}}{5-3\sqrt{3}}=\dfrac{\left(9-5\sqrt{3}\right)\left(5+3\sqrt{3}\right)}{\left(5-3\sqrt{3}\right)\left(5+3\sqrt{3}\right)}=\dfrac{45+2\sqrt{3}-45}{-2}=-\sqrt{3}\)
Thay \(x=7-4\sqrt{3}\) vào P, ta được:
\(P=\dfrac{7-4\sqrt{3}+2-\sqrt{3}}{6-3\sqrt{3}-1}\)
\(=\dfrac{9-5\sqrt{3}}{5-3\sqrt{3}}=-\sqrt{3}\)
b: \(5+2\sqrt{6}=\left(\sqrt{3}+\sqrt{2}\right)^2\)
c: \(13+\sqrt{48}=13+4\sqrt{3}=\left(2\sqrt{3}+1\right)^2\)
d: \(4+2\sqrt{3}=\left(\sqrt{3}+1\right)^2\)
\(13-4\sqrt{3}=\left(2\sqrt{3}\right)^2-2.2\sqrt{2}.1+1^2=\left(2\sqrt{3}-1\right)^2\)
a) \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
câu này \(\sqrt{15}\)đúng hơn \(\sqrt{5}\)
b) \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}=\frac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}\)c) \(\sqrt{5-2\sqrt{6}}-\sqrt{5+2\sqrt{6}}=\sqrt{3}-\sqrt{2}-\sqrt{3}-\sqrt{2}=-2\sqrt{2}\)
\(5+2\sqrt{6}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)
\(6+2\sqrt{5}=\sqrt{\left(\sqrt{5}+1\right)^2}\)
\(5+2\sqrt{6}=\left(\sqrt{3}+\sqrt{2}\right)^2\)
\(6+2\sqrt{5}=\left(\sqrt{5}+1\right)^2\)