Câu hỏi của hanhatphu

Question

$2\sqrt{37+20\sqrt{3}}$ - $\sqrt{73-40\sqrt{3}}$

Nguyễn Đức Trí · Accepted Answer

$2\sqrt[]{37+20\sqrt[]{3}}-\sqrt[]{73-40\sqrt[]{3}}$

$=2\sqrt[]{25+2.5.2\sqrt[]{3}+12}-\sqrt[]{48-2.5.4\sqrt[]{3}+25}$

$=2\sqrt[]{\left(5+2\sqrt[]{3}\right)^2}-\sqrt[]{\left(5-4\sqrt[]{3}\right)^2}$

$=2\left|5+2\sqrt[]{3}\right|-\left|5-4\sqrt[]{3}\right|$

$=2\left(5+2\sqrt[]{3}\right)-\left(4\sqrt[]{3}-5\right)\left(vì.4\sqrt[]{3}>5\right)$

$=10+4\sqrt[]{3}-4\sqrt[]{3}+5$

$=15$Câu trả lời: $2\sqrt[]{37+20\sqrt[]{3}}-\sqrt[]{73-40\sqrt[]{3}}$

$=2\sqrt[]{25+2.5.2\sqrt[]{3}+12}-\sqrt[]{48-2.5.4\sqrt[]{3}+25}$

$=2\sqrt[]{\left(5+2\sqrt[]{3}\right)^2}-\sqrt[]{\left(5-4\sqrt[]{3}\right)^2}$

$=2\left|5+2\sqrt[]{3}\right|-\left|5-4\sqrt[]{3}\right|$

$=2\left(5+2\sqrt[]{3}\right)-\left(4\sqrt[]{3}-5\right)\left(vì.4\sqrt[]{3}>5\right)$

$=10+4\sqrt[]{3}-4\sqrt[]{3}+5$

$=15$