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。～LeuNg FaN～ · 定居居民

聲明: 本人中三冇學過Quadratic Equations, 即使搵埋 New Trend Maths 3A, 3B都係冇...

1. Solve the following equations:
a) 6x^2+x-12=0
b) 12-11x-5x^2=0
c) 2y(y+1)+(y+3)(y-2)=12
d) (2x+1)/3 - (1/x) =2, where x not equal to zero.
e) 2x+(11root x) -6=0
f) 4^(x+1)- 18(2^x)+8=0
g) (2x-1)(x+1)=(x+1)
h) 5m^2-10mn+5n^2=20
*i) (2x+3)2=4(x-6)

*Q 1(i) 問題可能係: (2x+3)^2=4(x-6)

2. The sum of the squares of two consecutive odd number is 514, what is the smaller number?

3. Four squares, each side x cm, are cut from the corners of the rectangle in the figure. The remaining part is folded to for a cuboid. If its volume is 63 cm3, find the value of x.
*Figure ( 等於(=) 唔洗理佢...):
_x___6_____x_
↑┌┬──────┬┐ x
│├┘======└┤
10│=======│
│├┐======┌┤
↓└┴──────┴┘

5. A pilot flies 25km in the direction 146度 and then another 25km in the direction 270度. If he now flies back to the starting point in a straight line, find the distance and true bearing of his course.

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ALL questions MUST show the steps clearly.

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其實呢... 我成年F3 都冇學過...
唔知有冇人F3都係用new trend 又係有學過??
臨exam 整份咁既野... 都唔知考唔考... sosad
thx

FS1819 · 留學生

要S4先有架。其實quadratic只係首先factorize，之後話一個term係0或另一個term係0，再調個x嚟做subject。

e.g. 1(a)
6x²+x-12=0
(3x-4)(2x+3)=0
(3x-4)=0 or (2x+3)=0
x=4/3 or x=-3/2

TJ9504 · 版面管理員 C24-30

1d
2邊乘x^2, 再好似樓上咁計
1e
let y = root x
then y^2 = x

2.
let x be the smaller
then x+2 is the larger
x^2 + (x+2)^2 = 514
2x^2 + 4x+ 4 = 514
2x^2 + 4x -510= 0
x^2+ 2x - 255 = 0
(x+ 17) (x-15) = 0
x +17 = 0 or x-15 =0
x= -17 (reject) or x =15
so, the smaller number is 15
因為佢地係+ve odd number, 所以 -17 要reject

259B · 新移民

樓主, 以下回文for your reference only & supplement返FS1819兄ge 提及ge skill points
我好耐之前Form 3..
我果陣都有學Quardratic eqn.
但係唔會解文字題/ 要reject ans
其實解呢D題目唔難..
首先用你學過ge恆等式/ 十字相乘法因式分解2次式做2個數ge product...
eg. (x-A)(x-B) = 0
因為0乘任何1個數都係0
所以當2個數相乘 = 0果陣
有呢個結論:
其中1個數1定 = 0
所以好似FS1819兄所講
x-A =0 or x-B = 0
x= A or x = B
但切記1樣野..
RHS 1定要=0 先可以咁做
例如 (x-A)(x-B) = 8果陣
你要expand返開, 減個8過去再factorize佢先得
絕對唔可以寫成:
(x-A) = 8 or x-B =8
呢樣野絕對係錯的

希望幫到你理解..