# Quod Erat Demonstrandum

## 2017/08/12

### 重積求面積

Filed under: mathematics,NSS,University Mathematics — johnmayhk @ 6:10 下午
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1.某中四題：

## 2017/06/29

### 4

Filed under: Fun — johnmayhk @ 12:03 下午

$777=\sqrt{2}\displaystyle \sum_{k=1}^{777}k^2\cos(45^o+(k-2)90^o)$

$k^2-(k+1)^2-(k+2)^2+(k+3)^2$

## 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

## 2017/06/08

### 受保護的文章：放飛機

Filed under: Uncategorized — johnmayhk @ 5:17 下午

## 2017/05/28

### Transformation of graphs

Filed under: NSS,Teaching — johnmayhk @ 8:48 下午
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Share some points about the topic ‘transformation of graphs’. Nothing new.

Transformation of graphs in the HKDSE syllabus refers to

– translation
– reflection (with respect to the x-axis or the y-axis)
– enlargement or contraction (along the x-axis or the y-axis)

and all happen in the xy-plane.

(more…)

## 2017/05/27

### 帕斯卡三角形某結果

Filed under: Fun,Pure Mathematics — johnmayhk @ 8:56 上午
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## 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…)

## 2017/04/16

### 行列式特性

Filed under: NSS,Pure Mathematics — johnmayhk @ 5:05 下午
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Factorize $\left|\begin{array}{rcl}a &b &c\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$.

$\left|\begin{array}{rcl}a+b+c &a+b+c &a+b+c\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$

$=(a+b+c)\left|\begin{array}{rcl}1 &1 &1\\b+c &c+a &a+b \\a^2 &b^2 &c^2\\\end{array}\right|$

$\left|\begin{array}{rcl}a &b-a &c-a\\b+c &a-b &a-c \\a^2 &b^2-a^2 &c^2-a^2\\\end{array}\right|$

## 2017/04/05

### 答問

Filed under: Junior Form Mathematics — johnmayhk @ 11:11 下午
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$\displaystyle \frac{a}{(b-c)^2}+\frac{b}{(c-a)^2}+\frac{c}{(a-b)^2}=0$

$\displaystyle \frac{a}{b-c}+\frac{b}{c-a}+\frac{c}{a-b}$

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

## 2017/03/19

### 盛水水深

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 12:43 下午
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$(H-\sqrt[3]{H^3-h^3})$ 單位。

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