F.4 maths唔識><HELP please

2014-03-02 11:09 pm
1. Solve the following simultaneous equation.
x=4y+9 ......(1)
x=4-y^2 ......(2)

2. A two-digit positive integer is larger than the product of the two digits by 18. If the sum of the two digits is 13, find the integer.

3. Mr.Wong is 30 years older than his daughter. Two years ago, his age was the square of that of his daughter. Find the present age of Mr.Wong and his daughter.

回答 (1)

2014-03-03 12:17 am
✔ 最佳答案
1.
x=4y+9 ......(1)
x=4-y² ......(2)

equates (1) and (2)

4y+9 = 4-y²
y² + 4y + 5 = 0
using : [-b±√(b²-4ac)]/2a

y = [-4±√(16-20)]/2
y = (-2+4i) or (-2-4i)


2014-03-02 16:20:01 補充:
using : [-b±√(b²-4ac)]/2a

y = [-4±√(16-20)]/2
y = [-4±√(-4)]/2
y = [-4±(√4)(-1)]/2
y = [-4±(2)√(-1)]/2
y = (-2+i) or (-2-i)

2014-03-02 16:28:12 補充:
Let the number be XY

(10X+Y) - XY = 18 ...... (1)     [ e.g. 36 = 3X10 + 6 ]
X+Y = 13
X = 13-Y ......... (2)

Sub (2) into (1)

10(13-Y) + Y + (13-Y)Y = 18
130 - 10Y + Y + 13Y - Y² = 18
130 + 4Y - Y² = 18
Y² - 4Y - 112 = 0

2014-03-02 16:40:36 補充:
更正 :

Let the number be XY

(10X+Y) - XY = 18 ...... (1)     [ e.g. 36 = 3X10 + 6 ]
X+Y = 13
X = 13-Y ......... (2)

Sub (2) into (1)

10(13-Y) + Y - (13-Y)Y = 18
130 - 10Y + Y - 13Y + Y² = 18
130 - 22Y + Y² = 18
Y² - 22Y + 112 = 0
(Y-14)(Y-8)=0
Y=14 or Y=8

2014-03-02 16:42:28 補充:
When Y = 14 ; X+Y=13; X=-1 (reject)

When Y = 8; X+Y=13; X=5

The integer is 58

checking : 58 - 5X8 = 58 - 40 = 18

2014-03-02 16:50:30 補充:
3.

Let the present age of Mr.Wong and his daughter be W and D

W - D = 30
W = 30 + D .... (1)
(W-2) = (D-2)²
W-2=D²-4D+4 .... (2)

Sub (1) into (2)

(30+D) - 2 = D²-4D+4
D + 28 = D²-4D+4
D² - 5D -24 = 0
(D-8)(D+3) = 0
D = 8 or D = -3 (reject)

when D = 8 ; W = 30 + D ; W = 38

2014-03-02 16:51:53 補充:
Checking :

W - D = 38 - 8 = 30

2 years ago : W-2=36 ; D-2=6 ; 36 = 6²


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