✔ 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