căn (4+ 4căn3 +3)=a+b căn 3 tìm a^2 +b^2

2 câu trả lời

`\sqrt[4+4\sqrt[3]+3]=a+b\sqrt[3]`

`=>\sqrt[2^2+2.2\sqrt[3]+\sqrt[3]^2]=a+b\sqrt[3]`

`=>\sqrt[(2+\sqrt[3])^2]=a+b\sqrt[3]`

`=>|2+\sqrt[3]|=a+b\sqrt[3]`

`=>2+\sqrt[3]=a+b\sqrt[3]`

`=>a=2;b=1`

Vậy `a^2+b^2=2^2+1^2=4+1=5`

 

`\sqrt{4+4\sqrt{3}+3}=a+b\sqrt{3}`

`<=>\sqrt{2^2+2.2.\sqrt{3}+(\sqrt{3})^2}=a+b\sqrt{3}`

`<=>\sqrt{(2+\sqrt{3})^2}=a+b\sqrt{3}`

`<=>|2+\sqrt{3}|=a+b\sqrt{3}`

`<=>2+\sqrt{3}=a+b\sqrt{3}`

`<=>`$\begin{cases} a=2\\b=1 \end{cases}$

`=>a^2+b^2=2^2+1=4+1=5`

Vậy `a^2+b^2=5`

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