# Quod Erat Demonstrandum

## 2017/06/23

### 實數問題複數解決

Filed under: mathematics,NSS — johnmayhk @ 3:43 下午
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$(a^2+b^2)(c^2+d^2)=(ac-bd)^2+(ad+bc)^2$

## 2017/06/21

### 兩題二次方程

Filed under: mathematics,NSS — johnmayhk @ 6:28 下午
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1.

Refer to the figure below.

If $\alpha$ and $\beta$ are x-coordinates of P and Q respectively such that $\alpha^2+\beta^2=13$, find the value(s) of m.

$-x^2+3x-2=mx-8$
$x^2+(m-3)x-6=0$ (more…)

## 2017/06/10

### 正多邊形方程

Filed under: Additional / Applied Mathematics,Fun,mathematics,NSS — johnmayhk @ 12:24 下午
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https://www.desmos.com/calculator/vv7stc4nl0

## 2017/04/22

### 逆矩陣

Filed under: mathematics,NSS,University Mathematics — johnmayhk @ 11:10 下午
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$AB=BA=I$

## 2017/04/21

### 三垂線定理

Filed under: mathematics,NSS,Pure Mathematics,University Mathematics — johnmayhk @ 12:56 下午
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（一）前言

## 2017/04/17

### 人類總是

Filed under: mathematics — johnmayhk @ 6:12 下午

#無聊慎入

Solve $\frac{1}{2}(x-1)=3$.

$\frac{1}{2}x=3+1$ (more…)

## 2017/03/20

### 無聊 bonus

Filed under: mathematics,NSS — johnmayhk @ 9:55 上午
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Solve the following equations for real $x$.

1. $1+9^x+25^x=3^x+5^x+15^x$

2. $5^{x+1}+5(2^x)=3(10^x)+25^x+4^x+5$

## 2016/12/11

### 小心出題

Filed under: mathematics,NSS — johnmayhk @ 11:18 下午
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$AB=\sqrt{30^2+45^2-2(30)(45)\cos(60^o-40^o)}=19.7$ m

$AB=45\cos 40^o-30\cos 60^o=19.5$ m

## 2016/08/08

### 點解2

Filed under: Fun,mathematics — johnmayhk @ 11:12 下午
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$1+2+3+\dots +(n-1)+n+(n-1)+\dots +3+2+1=?$

$\frac{n(n+1)}{2}+\frac{(n-1)n}{2}=n^2$

$1+2+3+\dots +(n-1)+n+(n-1)+\dots +3+2+1=n^2$

## 2016/07/10

### 論商餘（三）

Filed under: mathematics,NSS,Teaching — johnmayhk @ 9:45 下午
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(a) 多項式與數字

## 2016/06/06

### 和扇形有關的某積分

Filed under: mathematics,NSS — johnmayhk @ 12:27 下午
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$\displaystyle \int^1_0\sqrt{1-x^2}dx$

$\displaystyle \int^1_0\sqrt{1-x^2}dx=\frac{\pi}{4}$

$\displaystyle \int_0^t\sqrt{1-x^2}dx$　（其中 $0 < t < 1$

$x=\sin\theta$ 又或用部分積分吧。但以圖示之，求上述積分，即是求下圖著色部分面積：

(more…)

## 2016/04/07

### log y to the base a

Filed under: Fun,mathematics — johnmayhk @ 4:11 下午

（想畫公仔，不喜勿插）

15，16 世紀某天。三條書局友，在表面寧靜的式子…

(more…)

## 2016/02/15

### 某 front view

Filed under: Junior Form Mathematics,mathematics — johnmayhk @ 2:38 下午

## 2015/07/07

### 某關於整除的題

Filed under: mathematics,NSS — johnmayhk @ 3:06 下午
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$(n^2)!$

$(n!)^{n+1}$

(more…)

## 2015/03/07

### 幾條正三角形

Filed under: mathematics,NSS — johnmayhk @ 8:59 下午
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