√(4+4 √3 +3) = a +b √3 tìm a ²+b ²

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`~rai~`

\(\sqrt{4+4\sqrt{3}+3}=a+b\sqrt{3}\\\Leftrightarrow \sqrt{2^2+2.2\sqrt{3}+(\sqrt{3})^2}=a+b\sqrt{3}\\\Leftrightarrow \sqrt{(2+\sqrt{3})^2}=a+b\sqrt{3}\\\Leftrightarrow |2+\sqrt{3}|=a+b\sqrt{3}\\\Leftrightarrow 2+\sqrt{3}=a+b\sqrt{3}\quad\text{(vì }2+\sqrt{3}>0)\\\Leftrightarrow \begin{cases}a=2\\b=1\end{cases}\\\Rightarrow a^2+b^2=2^2+1^2=5.\\\text{Vậy }a^2+b^2=5.\)

Bạn tham khảo

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

`<=>\sqrt{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}`

`=>{(a=2),(b=1):}`

Vậy `a^2+b^2<=>2^2+1^2=5`

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