Question

\(\text{Chứng minh rằng:}\)

\(\text{a) }\) \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)

\(\text{b)}\) \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)

Answer 1

`a)` Có: `VP=(\sqrt{5})^2+2.\sqrt{5}.2+2^2=5+4\sqrt{5}+4=9+4\sqrt{5}=VT`

    `->Đpcm`

`b)` Có:`VT=\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{(\sqrt{5})^2-2.\sqrt{5}.2+2^2}-\sqrt{5}`

       `=\sqrt{(\sqrt{5}-2)^2}-\sqrt{5}=|\sqrt{5}-2|-\sqrt{5}`

                 `=\sqrt{5}-2-\sqrt{5}=-2=VP`

 `->Đpcm`

Answer 2

a) \(9+4\sqrt{5}=5+2.2.\sqrt{5}+2^2=\left(\sqrt{5}+2\right)^2\\ b.\sqrt{9-4\sqrt{5}}=\sqrt{5-4\sqrt{5}+4}=\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-2=>\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)

Answer 3

a) \(Ta\) \(có:\)

\(9+4\sqrt{5}=\left(\sqrt{5}\right)^2+2.2.\sqrt{5}+2^2=\left(\sqrt{5}+2\right)^2\)

Vậy \(9+4\sqrt{5}=\left(\sqrt{5}+2\right)^2\)

b) \(Ta\) \(có:\)

\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}=\left|\sqrt{5}-2\right|-\sqrt{5}=-2+\sqrt{5}-\sqrt{5}=-2\)

Vậy \(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)