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# If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 54376
If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?  [#permalink]

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10 Apr 2019, 21:47
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Difficulty:

15% (low)

Question Stats:

89% (00:45) correct 11% (02:25) wrong based on 27 sessions

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If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?

(A) –1
(B) 0
(C) 1
(D) 3
(E) 4

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Re: If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?  [#permalink]

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11 Apr 2019, 00:49
Bunuel wrote:
If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?

(A) –1
(B) 0
(C) 1
(D) 3
(E) 4

simplify x^2 – 4x + 3 = 0
we get x= 3,1
so (x – 2)^2
1 IMO C
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Re: If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?  [#permalink]

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11 Apr 2019, 01:01
A very easy method would be to use the following formula

$$(a-b)^2 = a^2 + b^2 -2ab$$

$$(x-2)^2 = x^2 + 4 - 4x$$
This can also be written as

$$(x-2)^2$$ = $$x^2 - 4x + 3$$ $$+ 1$$ ........... (1)

We are given that
$$x^2 - 4x + 3 = 0$$

Re writing (1) as
$$(x-2)^2 = 0 + 1$$
$$(x-2)^2 = 1$$

Hence, C
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Re: If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?  [#permalink]

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11 Apr 2019, 01:13

We are given that
x^2−4x+3=0
When we solve this equation we get 2 values of x, 3 and 1.

Substitute 3 and 1 into (x-2)^2. In both cases, you get 1. Hence, the answer is C

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Re: If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?  [#permalink]

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13 Apr 2019, 19:20
Bunuel wrote:
If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?

(A) –1
(B) 0
(C) 1
(D) 3
(E) 4

We see that (x + 2)^2 = x^2 - 4x + 4

Since x^2 - 4x = -3, we have:

-3 + 4 = 1

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Re: If x^2 – 4x + 3 = 0, then what is the value of (x – 2)^2 ?   [#permalink] 13 Apr 2019, 19:20
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