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605-655 (Medium)|   Algebra|   Exponents|      
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xhimi
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 05 Dec 2013, 20:41
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45% (medium)

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72% (02:25) correct 28% (02:55) wrong based on 453 sessions

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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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Official Answer
A
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mau5
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 05 Dec 2013, 21:48
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xhimi
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?
Show more

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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KarishmaB
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 05 Dec 2013, 21:42
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xhimi
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?
Show more

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))

Answer (A)
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 05 Dec 2013, 21:59
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I got lost in the algebraic approach, so thanks for showing both ways Karishma and Mau5
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PareshGmat
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 11 Apr 2014, 01:44
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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

Answer = A
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 11 Apr 2014, 02:25
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xhimi
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?
Show more

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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If (x-p)^2 - (x-t)^2 / t-p = x-t and 28 Jul 2020, 06:12
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If (x-p)^2 - (x-t)^2 / t-p = x-t and 20 Aug 2025, 07:35
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