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If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for

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Manager
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Joined: 10 Oct 2008
Posts: 56
If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for [#permalink]

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New post 10 Oct 2008, 09:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

x^2 +b^x+c=x^2+2xd+d^2 bx-2xd=d^2-c x( b-2d)=d^2-c

Stm1 d=3 x(b-6)=9-c insufficient
Stm2 b=6 x(6-2d)=d^2-c insufficient
Combine stm1 and stm2
c=3 the answer is C. Is that correct?
Manager
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Re: discuss a math problem [#permalink]

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New post 10 Oct 2008, 10:12
I think the answer is (E)

you have 4 unknowns

b,c,d,x

even if you know what d,b are then you are left with

\(x^2+6^x+c = (x+3)^2\)

\(x^2+6^x+c = x^2+6x+9\)

\(6^x+c=6x+9\)

cannot be solved

x can be 1 and c can be 9 or x can be 2 and c can be -15

:)
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Re: discuss a math problem [#permalink]

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New post 10 Oct 2008, 12:13
Jcpenny wrote:
If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6


First, I'm absolutely certain that the question should read:

If b, c, and d are constants and x^2 + bx + c = (x+d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6


because otherwise it's mathematically impossible that what is stated in the stem is true, unless b = 1, d = 0 and c = -1. Proceeding on that assumption:

We know that

\(x^2 + bx + c = (x+d)^2\)

for all values of x. In particular, it's true for x=0:

\(0^2 + b*0 + c = (0+d)^2 \\
c = d^2\)

So you can find c if you know d, and Statement 1 is sufficient.

Further, knowing that \(c = d^2\), we have

\(x^2 + bx + d^2 = (x+d)^2 \\
x^2 + bx + d^2 = x^2 + 2dx + d^2 \\
bx = 2xd \\
b = 2d \\\)

so if you can find b, you can find d, and therefore you can find c. Statement 2 is sufficient.
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Re: discuss a math problem   [#permalink] 10 Oct 2008, 12:13
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