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If (x-1)^2=(x-2)^2, then x=

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Carcass
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If (x-1)^2=(x-2)^2, then x= [#permalink] New post   Updated on: 03 Jan 2024, 04:36
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If \((x-1)^2=(x-2)^2\), then \(x=\)

A. -5/8

B. 5/3

C. 4/3

D. 3/2

E. 5/2
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D

Originally posted by Carcass on 11 Dec 2020, 22:19.
Last edited by Carcass on 03 Jan 2024, 04:36, edited 1 time in total.
Fixed typo
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   12 Dec 2020, 03:17
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the answer is 3/2 !!
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   12 Dec 2020, 08:13
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(x-1)^2 = (x-2)^2
Factoring each side, we get
x^2-2x+1= x^2-4x+4 subtract (x^2) for both side
-2x+1=-4x+4 add +4x for both sides and subtract 1
2x= 3 ==> x= 3/2.

and it is true that (3/2-1)^2 = (3/2-2)^2
0.5^2 = -0.5^2
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   16 Dec 2020, 21:49
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(x-1)^2 = (x-2)^2

We know that quadratic curves are symmetric. so what number ends up same magnitude when you subtract 1 and 2 from it?

1.5 because 1.5-1 = .5 and 1.5-2 = -.5. (squaring cancels the negative 1)
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 00:38
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if \((x-1)^ = (x-2)^2\) then,

expanding both sides of the equation, we get

\(x^2 + 1^2 - 2\times 1\times x = x^2 + 2^2 - 2\times 2 \times x\)

\(x^2 + 1 - 2x = x^2 + 4 - 4x\)

cancelling like terms on both sides and rearranging,

\(2x - 3 = 0\)

\(2x = 3\)

\(x = \frac{3}{2}\)
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 03:09
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Hi

There is a typo in option D. It should be 3/2.

Thanks

Carcass wrote:
If \((x-1)^2=(x-2)^2\), then \(x=\)

A. -5/8

B. 5/3

C. 4/3

D. 2/3

E. 5/2
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Re: If (x-1)^2=(x-2)^2, then x= [#permalink] New post   03 Jan 2024, 04:36
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the book had the typo

thanks sir fixed
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