S4數學題目(2) - Ans.fyi 參考答案

S4數學題目(2)

[匿名]

2012-08-23 7:45 pm

1. 3+4i is aroot of the equation 5x2次+bx+c=0

(a) find the other root of the equation
(b) find the values of b and c

2. a piece of 32cm long wire is cut into two parts such that the length of one part
is x cm .If we bend each part to form a square respectively , then what is the
value of x such that the sum of the areas of the sqaures the least ?

回答 (1)

用戶2053

2012-08-25 9:00 pm

✔ 最佳答案

1a)The other root is 3 - 4i. (因為虛根一定是共軛的, 即 3 ± 4i 的形式)b)Sum of roots =
(3 + 4i) + (3 - 4i) = - b/5
6 = - b/5
b = - 30Product of roots =
(3 + 4i) (3 - 4i) = c/5
9 + 16 = c/5
c = 125

2)One part is x , another part is 32 - x.One part form a square with side x/4 ,
another part form a square with side (32 - x)/4The sum of the areas of the sqaures
= (x/4)² + ( (32 - x)/4 )²
= (x/4)² + (8 - x/4)²
= (x/4)² + (x/4)² - 2(8)(x/4) + 64
= 2 [ (x/4)² - 8(x/4) + 32 ]
= 2 [ (x/4)² - 2(4)(x/4) + 4² - 4² + 32 ] ... 配方法
= 2 [ (x/4 - 4)² - 4² + 32 ]
= 2 [ (x/4 - 4)² + 16 ]When x/4 = 4 , the least sum of the areas of the sqaures
= 2 [ 0 + 16 ] = 32cm²

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