a*****g
发帖数: 1320 | 1 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
标 题: mathscounts 数学题求助(4)
发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x=3=
0. What are the value of b and c? Express your answer as an ordered pair (b,
c)
2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
=5. What are the value of b, c, and d? Express your answer as an ordered
triple (b,c,d)
3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
Express your answer as a common fraction
4) What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
5) The solutions of X3-63x2+cx-1728=0 form a geometric sequence. What is the
value of c?
Thanks a lot! | Y****a
发帖数: 243 | 2 闲着无聊，来玩玩
3=
b,
expend (x-5)^2+7(x-5)+3=0, you will get the value of b and c
x
expend (x-3)(x-4)(x-5)=0 , you will get the value of b c & d
【在 a*****g 的大作中提到】
: 【 以下文字转载自 SanFrancisco 讨论区 】
: 发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
: 标 题: mathscounts 数学题求助(4)
: 发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
: 1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x=3=
: 0. What are the value of b and c? Express your answer as an ordered pair (b,
: c)
: 2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
: =5. What are the value of b, c, and d? Express your answer as an ordered
: triple (b,c,d)
| Y****a
发帖数: 243 | 3 3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
Express your answer as a common fraction
answer is 3 ?
4) What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
159 ? | Y****a
发帖数: 243 | 4 5) The solutions of X3-63x2+cx-1728=0 form a geometric sequence. What is the
value of c?
the solutions are 3,12,48
c=3*12+3*48+12*48=756 | Y****a
发帖数: 243 | 5 哦，3） 把题看错了，这个不对
【在 Y****a 的大作中提到】
: 3) What is the sum of the reciprocals of the solutions of x3-3x2-13x+15=0?
: Express your answer as a common fraction
: answer is 3 ?
: 4) What is the sum of the squares of the solutions of x3-15x2+66x-80=0?
: 159 ?
| T********d
发帖数: 621 | 6 1
b = 5x7 = 35, c = 5^2 x 3 = 25x3 = 75
2.
(x-3)(x-4)(x-5) = 0 ->
b = -12
c = 47
d=-60
3.
if x=a, b , c are the solution
then: (1/a) + (1/b) + (1/c)
= (ab+ac+bc)/(abc)
(ab+ac+bc) = -13
abc = -15
Therefore, solution is 13/15
4.
If x = a,b, c are the solution
Thena^2 + b^2 + c^2 = (a+b+c)^2 - 2 (ab+bc+ac) = 15^2 - 2(66) = 93
5.
if x = a, b, c are the solution
Then abc = 1728
a+b+c = 63
ab + bc + ac = C
and b/c = c/b -> b^2 = ac
-> abc = b^3 =1728 -> b = 12
-> ac = 144 and a+c = 51
C = ab+bc+ac = b(a+c) + ac = 12x51 + 144 = 756
Key is:
solution for X^3 equation X = a, b, c
X^3 -(a+b+c)X^2 + (ab+ac+bc)X - abc = 0
3=
b,
x
【在 a*****g 的大作中提到】
: 【 以下文字转载自 SanFrancisco 讨论区 】
: 发信人: ashuang (东洛杉矶推妈+股票大妈), 信区: SanFrancisco
: 标 题: mathscounts 数学题求助(4)
: 发信站: BBS 未名空间站 (Wed Jan 19 00:02:32 2011, 美东)
: 1) The solutions of x2 +bx+c=0 are each 5 more than the solution of x2+7x=3=
: 0. What are the value of b and c? Express your answer as an ordered pair (b,
: c)
: 2) A cubic equation of the form x3+ bx2+cx+d==0 has solutions x=3, x=4 and x
: =5. What are the value of b, c, and d? Express your answer as an ordered
: triple (b,c,d)
| a*****g
发帖数: 1320 | 7 Super many thanks you guys great help!! | m**********g
发帖数: 114 | 8 好难啊
x2+7x=3=
(b,
and x
ordered
13x+15=0?
【在 a*****g 的大作中提到】
: Super many thanks you guys great help!!
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