# Quod Erat Demonstrandum

## 2008/02/23

### Quadratic formula program @ CASIO 3950p/3650p

Filed under: HKCEE,Junior Form Mathematics — johnmayhk @ 11:17 下午
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Factorize $4x^2 - 4xy + y^2$.

（不變金句：教了，不等於學了）

(1) Factorize $6x^2 - 6y^2 + 5xy$

$6x^2 + 5xy - 6y^2$

$a=6, b=5, c=-6$

2┘3 及 -3┘2

$\frac{2}{3}, -\frac{3}{2}$

$6x^2 + 5xy - 6y^2$
= $6(x - ?)(x - ?)$

$6x^2 + 5xy - 6y^2$
= $6(x - \frac{2}{3}y)(x - (-\frac{3}{2}y))$
= $3\times2(x - \frac{2}{3}y)(x - (-\frac{3}{2}y))$
= $(3x - 3(\frac{2}{3}y))(2x - 2(-\frac{3}{2}y))$
= $(3x - 2y)(2x + 3y)$

(2) Factorize $15x^2 + xy^2 - 2y^4$

$15x^2 + xy^2 - 2y^4$
= $15x^2 + x(y^2) - 2(y^2)^2$

Enter $a=15, b=1, c=-2$ into calculator, the answer will be

-2┘5 , 1┘3

Hence

$15x^2 + xy^2 - 2y^4$
= $15x^2 + x(y^2) - 2(y^2)^2$
= $15(x - (-\frac{2}{5}y^2))(x - \frac{1}{3}y^2)$
= $(5x - 5(-\frac{2}{5}y^2))(3x - 3(\frac{1}{3}y^2))$
= $(5x + 2y^2)(3x - y^2)$

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

http://lpl.hkcampus.net/~lpl-wwk/

## 3 則迴響 »

1. 感謝你, 我一直在找, 現在有program用了-)

迴響 由 thankyouverymuch — 2011/06/12 @ 11:00 下午 | 回應

2. I remember a few years ago when I learnt the quadratic formula, I swore I would not use the programme as I always wanted to rely on my own, to rely on my memory, entering every number, every operation sign by my fingers. Now, I have to break my promise just because I have to get fast in the exam…

迴響 由 Bruce Leung — 2012/11/08 @ 11:08 下午 | 回應

3. Now I have even surrendered to Heron’s formula and I don’t even bother to memorize radius = sqrt(D^2 / 4 + E^2 / 4 – F) for a circle in general form. What a degeneration of my brain.

迴響 由 Bruce Leung — 2012/11/08 @ 11:10 下午 | 回應