問題: 解聯立方程 (中二)
這題解聯立方程的題目除考大家識唔識解聯立方程之外，仲考驗大家識唔識得變通。解b部的重點在於留意到b部中的兩條方程其實與a部的方程基本上係一樣的,只係把x、y改寫成 (dfrac{1}{a})及(dfrac{1}{b})。a) (begin{align}&quad 2x-5y=-3 ...... (1) \&quad 3x+y=1 ...... (2) \&(2)times 5:\&quad 15x+5y=5 ...... (3) \&(1)+(3):\&a...
問題: 平面幾何 (平行四邊形+相似三角形)
Consider △CPB and △BPM, ∠CPM = ∠BPM = 90º (given) ∠PMB = 180º - ∠BPM - ∠PBM = 90º - ∠PBM ∠PBC = ∠MBC - ∠PMB = 90º - ∠PBM ∴, ∠PMB = ∠PBC Therefore, △CPB ∼ △BPM (A.A.A. ∼). Now, consider △CPD and △BPN, ∠DCP = ∠DCB - ∠P...
問題: 指數定律+科學記數法
今日喺Facebook見到有人問咗一條看似簡單, 但係又唔可以就咁用計數機㩒個答案出嚟嘅數。想喺依度同大家分享一吓:(begin{align}&dfrac{84^{90}-64^{80}}{20^{70}} \&= dfrac{84^{90}}{20^{70}}-dfrac{64^{80}}{20^{70}} \&= (dfrac{84^{9}}{20^{7}})^{10}-(dfrac{64^{8}}{20^{7}})^{10} \&= (162668553.5...