Câu hỏi của Mai Xuân Phong

Question

Tính

$x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}$

Mysterious Person · Accepted Answer

x = $\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}$

x = $\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}.3+3^2}$ - $\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+3^2}$

x = $\sqrt{\left(2\sqrt{5}+3\right)^2}$ - $\sqrt{\left(2\sqrt{5}-3\right)^2}$

x = $|$ $2\sqrt{5}+3$ $|$ - $|$ $2\sqrt{5}-3$ $|$

x = $\left(2\sqrt{5}+3\right)-\left(2\sqrt{5}-3\right)$

x = $2\sqrt{5}+3-2\sqrt{5}+3$ = 6Câu trả lời: x = $\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}$

x = $\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}.3+3^2}$ - $\sqrt{\left(2\sqrt{5}\right)^2-2.2\sqrt{5}.3+3^2}$

x = $\sqrt{\left(2\sqrt{5}+3\right)^2}$ - $\sqrt{\left(2\sqrt{5}-3\right)^2}$

x = $|$ $2\sqrt{5}+3$ $|$ - $|$ $2\sqrt{5}-3$ $|$

x = $\left(2\sqrt{5}+3\right)-\left(2\sqrt{5}-3\right)$

x = $2\sqrt{5}+3-2\sqrt{5}+3$ = 6

Sáng · Answer

$x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}$

$\Rightarrow x=\sqrt{\left(3+2\sqrt{5}\right)^2}-\sqrt{\left(3-2\sqrt{5}\right)^2}$

$\Rightarrow x=3+2\sqrt{5}-\left(2\sqrt{5}-3\right)$

$\Rightarrow x=3+2\sqrt{5}-2\sqrt{5}+3$

$\Rightarrow x=6$Câu trả lời: $x=\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}$

$\Rightarrow x=\sqrt{\left(3+2\sqrt{5}\right)^2}-\sqrt{\left(3-2\sqrt{5}\right)^2}$

$\Rightarrow x=3+2\sqrt{5}-\left(2\sqrt{5}-3\right)$

$\Rightarrow x=3+2\sqrt{5}-2\sqrt{5}+3$

$\Rightarrow x=6$