2 câu trả lời
`~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`
Câu hỏi trong lớp
Xem thêm