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S4 Math
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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... 顯示更多 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?
最佳解答:
1)Let x be the number x^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
其他解答:
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
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