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# If (x-p)^2 - (x-t)^2 / t-p = x-t and

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If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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05 Dec 2013, 19:41
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If $$\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t$$ and $$t\neq{p}$$ , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?
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Joined: 10 Oct 2012
Posts: 562
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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05 Dec 2013, 20:48
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1
xhimi wrote:
If $$\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t$$ and $$t\neq{p}$$ , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?

We know that$$a^2-b^2 = (a-b)*(a+b)$$

Thus, $$\frac{(x-p)^2 - (x-t)^2}{t-p} = \frac{(x-p+x-t)*[(x-p)-(x-t)])}{t-p} \to \frac{(2x-p-t)*(t-p)}{t-p}$$

As $$t\neq{p}$$ , we can cancel it from both Numerator and Denominator, and we get $$2x-p-t = x-t \to x = p$$

A.
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Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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05 Dec 2013, 20:42
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1
xhimi wrote:
If $$\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t$$ and $$t\neq{p}$$ , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?

I would put values for t and p such that each option gives a different answer. Say, t= 3, p = 1. Every option gives a different answer so when I put these values in the equation, I will get my answer for sure.

$$\frac{(x-1)^2 - (x-3)^2}{3-1} = x-3$$

$$\frac{4x - 8}{3-1} = x-3$$

$$2x - 4 = x - 3$$

x = 1
Only option (A) gives 1 when we put t = 3, p = 1 in the options. So x must be equal to p (which is option (A))

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Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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05 Dec 2013, 20:59
I got lost in the algebraic approach, so thanks for showing both ways Karishma and Mau5
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Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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11 Apr 2014, 00:44
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$$x^2 - 2xp + p^2 - (x^2 - 2xt + t^2) = xt - xp - t^2 + pt$$

(2x - x) * (t-p) = p * (t-p)

x = p

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Posts: 114
Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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11 Apr 2014, 01:25
1
xhimi wrote:
If $$\frac{(x-p)^2 - (x-t)^2}{t-p} = x-t$$ and $$t\neq{p}$$ , then x=

A) p
B) t
C) p-2t
D) t+p
E) t-p

What is the best approach to solve for x?

If t = 3 and p = 2 then

(x - 2)^2 - (x - 3)^2 = (x - 3) (3 - 2)

x^2 + 4 - 4x - x^2 - 9 + 6x = x - 3

2x - 5 = x - 3

x = 2

Hence x = p
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Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and  [#permalink]

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28 Jul 2020, 05:12
Any similar questions?
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Re: If (x-p)^2 - (x-t)^2 / t-p = x-t and   [#permalink] 28 Jul 2020, 05:12