Please to slove the following question.
[請詳細烈式]
1. The sum of a number and its square is 72. Find all possible numbers.
2. Two odd numbers differ by 18. If their product is 63, find the two numbers.
3. The area of a triangle is 18cm^2. If the base of the triangle is 5 cm
shorter than its height, find the base of the triangle.
4. The perimeter and the area of a rectangle are 44cm and 112cm
respectively. Find the length and the width of the rectangle.
5.Daisy is 2 years older than her brother. Two years later, the product
of the ages of Daisy and her brother woll be three times her age. How
old is Daisy now?
S4 Math
2011-07-20 6:41 am
回答 (2)
2011-07-20 7:01 am
✔ 最佳答案
1)Let x be the numberx^2+x=72
x^2+x-72=0
跟住禁機
x=8同-9
2)Let the smaller number be x
x(x+18)=63
x^2+18x-63=0
跟住禁機
x=3同-21
3)Let the height be x
x(x-5)/2=18
x^2-5x=36
x^2-5x-36=0
then禁機
4)Let the length and width be x and y respectively
2(x+y)=44
x+y=22
x=22-y --(i)
xy=112 --(ii)
Sub (i) into (ii)
(22-y)y=112
22y-y^2=112
y^2-22y+112=0
禁機
5)Let Daisy is x years old
(x+2)(x-2+2)=3x
x^2+2x-3x=0
x^2-x=0
禁機
2011-07-20 7:10 am
1.
let the number be a.
a+a^2=72
a^2+a-72=0
(a+9)(a-8)=0
a=-9 or a=8
all possible numbers are -9,8 2.
let the two number be m,n
m-n=18
mn=63 So,
m=n+18
(n+18)(n)=63
n^2+18n-63=0
(n+21)(n-3)=0
n=-21 or n=3when n=-21,
m=-21+18=-3when n=3,
m=3+18=21the two numbers are (-3 and -21) or (21 and 3)3.
let the base of the triangle be b cm
base*height/2=area
b*(b+5)/2=18
b^2+5b-36=0
(b+9)(b-4)=0
b=-9 (rejected) or b=4 4.
let the length be a cm,the width be b cm
where a>=b
2a+2b=44
ab=112 So,a+b=22
a=22-b
(22-b)(b)=112
22b-b^2=112
b^2-22b+112=0
(b-8)(b-14)=0
b=8 or b=14when b=8,
a+8=22
a=14when b=14,
a+14=22
a=8 (rejected)So, the length is 14cm,the width is 8cm5.
let the age of Daisy be x now
the age of her brother now is x-2 (x+2)(x-2+2)=3(x+2)
(x+2)(x)=3(x+2)
x^2+2x=3x+6
x^2-x-6=0
(x-3)(x+2)=0
x=3 or x=-2(rejected)So, Daisy is 3 years old now
let the number be a.
a+a^2=72
a^2+a-72=0
(a+9)(a-8)=0
a=-9 or a=8
all possible numbers are -9,8 2.
let the two number be m,n
m-n=18
mn=63 So,
m=n+18
(n+18)(n)=63
n^2+18n-63=0
(n+21)(n-3)=0
n=-21 or n=3when n=-21,
m=-21+18=-3when n=3,
m=3+18=21the two numbers are (-3 and -21) or (21 and 3)3.
let the base of the triangle be b cm
base*height/2=area
b*(b+5)/2=18
b^2+5b-36=0
(b+9)(b-4)=0
b=-9 (rejected) or b=4 4.
let the length be a cm,the width be b cm
where a>=b
2a+2b=44
ab=112 So,a+b=22
a=22-b
(22-b)(b)=112
22b-b^2=112
b^2-22b+112=0
(b-8)(b-14)=0
b=8 or b=14when b=8,
a+8=22
a=14when b=14,
a+14=22
a=8 (rejected)So, the length is 14cm,the width is 8cm5.
let the age of Daisy be x now
the age of her brother now is x-2 (x+2)(x-2+2)=3(x+2)
(x+2)(x)=3(x+2)
x^2+2x=3x+6
x^2-x-6=0
(x-3)(x+2)=0
x=3 or x=-2(rejected)So, Daisy is 3 years old now
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