Question

Rút gọn biểu thức sau

(3\ +\ \frac{\frac{9}{2}}{\sqrt5}\ )\times\ ( 2-\sqrt5 )n + (3\ -\ \frac{\frac{9}{2}}{\sqrt5}) \times(2+\sqrt5 )

Answer 1

Explanation:

`\left(3+((9)/(2))/(√(5))\right)\left(2-√(5)\right)n+\left(3-((9)/(2))/(√(5))\right)\left(2+√(5)\right)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad ((b)/(c))/(a)=(b)/(c\:* \:a)`

`=\left((9)/(2√(5))+3\right)\left(2-√(5)\right)n+\left(-((9)/(2))/(√(5))+3\right)\left(2+√(5)\right)`

`\mathrm{Apply\:the\:fraction\:rule}:\quad ((b)/(c))/(a)=(b)/(c\:* \:a)`

`=\left((9)/(2√(5))+3\right)\left(2-√(5)\right)n+\left(-(9)/(2√(5))+3\right)\left(2+√(5)\right)`

`=(-12-9√(5))/(2√(5))n+6n+\left(3-(9)/(2√(5))\right)\left(2+√(5)\right)`

`=(-12-9√(5))/(2√(5))n+6n+(12-9√(5))/(2√(5))+6`

`=(√(5)\left(\left(3√(5)-12\right)n+12-9√(5)\right))/(10)+6`