1.In a two-digit number, the units digit is greater than the tens digit by 3, and the sum of the squares of the two digits is greater than the two-digit number by 3. Let the units digit be x.
(a)Express, in terms of x,
(i) the tens digit
(ii) the value of the two-digit number.
(b) Hence, find the two-digit number.
2. Joan is 2 years younger than her brother Matthew, and 32 years younger than her father. Three years ago, the product of the ages of Joan and Matthew was exactly 2 times the age of their father. How old is Matthew now?
3. If a and b are the roots of 2x^2-9x+8=0, where a>b, form a quadratic equation with roots (a-2) and (b+2). Leave the coefficients and/or the constant term in radical sign if necessary.
F4 maths (Quadratic) (急~~!)
2009-11-20 4:46 am
回答 (2)
2009-11-20 7:15 am
✔ 最佳答案
1a(i) (x-3)(ii) 10(x-3)+x
b.
x^2+(x-3)^2-[10(x-3)+x]=3
x^2+x^2-6x+9-10x+30-x=3
2x^2-17x+36=0
(2x-9)(x-4)=0
x=4.5(rejected) or 4
The two-digit number = 10[(4)-3]+(4)=14
2.
Let the age of Matthew be x,
then Joan's age is (x-2) and his father's age is (x+30)
(x-3)[(x-2)-3]=2[(x+30)-3]
(x-3)(x-5)=2(x+27)
x^2-8x+15=2x+54
x^2-10x-39=0
(x-13)(x+3)=0
x=13 or -3(rejected)
The age of Matthew is 13.
3.
a+b= (-9/2),
ab=8/2=4,
The required equation is
[x-(a-2)][x-(b+2)]=0
x^2-(b+2)x-(a-2)x+(a-2)(b+2)=0
x^2-(a+b)x+(ab+2a-2b-4)=0
x^2+(9/2)x+{(4)+開方[(2a+2b)^2-8ab]-4}=0
2x^2+9x+開方[(9)^2-8(4)]=0
2x^2+9x+7=0
2009-11-19 23:15:28 補充：
第三題唔係好肯定
2009-11-19 23:17:15 補充：
第二題
個句亂碼你當係the age of Joan is x-2 and the age of his father is x+30就得
2009-11-19 23:27:14 補充：
Sorry
第三題應該係
[x-(a-2)][x-(b+2)]=0
x^2-(b+2)x-(a-2)x+(a-2)(b+2)=0
x^2-(a+b)x+(ab+2a-2b-4)=0
x^2+(9/2)x+{(4)+2*開方[(a+b)^2-4ab]-4}=0
2x^2+9x+4*開方[(81/4)-4(4)]=0
2x^2+9x+4*開方[(81-64)/4]=0
2x^2+9x+4/2*開方(81-64)=0
2x^2+9x+2*(開方17)=0
2009-11-21 4:28 am
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