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

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07 Apr 2019, 21:55
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Difficulty:

15% (low)

Question Stats:

88% (00:42) correct 12% (01:07) wrong based on 25 sessions

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

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

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Joined: 31 Oct 2013
Posts: 1322
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If x^2 – 4x + 3 equals 0, then what is the value of (x – 2)^2 ?  [#permalink]

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07 Apr 2019, 22:17
Bunuel wrote:
If $$x^2 – 4x + 3$$ equals 0, then what is the value of $$(x – 2)^2$$ ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

Given,

$$x^2 – 4x + 3$$ = 0

( x - 3) ( x - 1) = 0

x = 3

or

x = 1.

now,

$$(x - 2)^2 = ( 1 - 2 )^2 = (-1)^2 = 1$$

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

Intern
Joined: 04 Aug 2016
Posts: 8
Re: If x^2 – 4x + 3 equals 0, then what is the value of (x – 2)^2 ?  [#permalink]

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08 Apr 2019, 00:16
We have x^2-4x+3=0

Now (x-2)^2= x^2-4x+4

So we need to add 1 in the first equation.
So the answer will be x^2-4x+3+1=1
So (x-2)^2=1

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

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08 Apr 2019, 00:22
Bunuel wrote:
If $$x^2 – 4x + 3$$ equals 0, then what is the value of $$(x – 2)^2$$ ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

$$x^2 – 4x + 3$$ equals 0
(x-3)(x-1) or say x=+3,+1
so $$(x – 2)^2$$
+1 always
IMO B
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Joined: 26 Mar 2013
Posts: 2136
If x^2 – 4x + 3 equals 0, then what is the value of (x – 2)^2 ?  [#permalink]

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08 Apr 2019, 03:18
Bunuel wrote:
If $$x^2 – 4x + 3$$ equals 0, then what is the value of $$(x – 2)^2$$ ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

$$(x – 2)^2$$ = $$x^2 – 4x + 4= a$$...........1

.................$$x^2 – 4x + 3= 0$$...........2
--------------------------------------------------------------------Subtracting

a =1

Intern
Joined: 24 Mar 2016
Posts: 17
If x^2 – 4x + 3 equals 0, then what is the value of (x – 2)^2 ?  [#permalink]

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08 Apr 2019, 09:46
Bunuel wrote:
If $$x^2 – 4x + 3$$ equals 0, then what is the value of $$(x – 2)^2$$ ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

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

x^2 - 4x + 3 = 0

(x - 2)^2 - 1= 0
(x - 2)^2 = 1

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

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10 Apr 2019, 17:54
Bunuel wrote:
If $$x^2 – 4x + 3$$ equals 0, then what is the value of $$(x – 2)^2$$ ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

Factoring the given quadratic we have:

(x - 3)(x - 1) = 0

x = 3 or x = 1

Thus, (x - 2)^2 is 1^1 or (-1)^2, both of which equal 1.

Alternate solution:

We see that (x - 2)^2 = x^2 - 4x + 4, which is 1 more than x^2 - 4x + 3. Since x^2 - 4x + 3 = 0, so (x - 2)^2 must be 1.

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Re: If x^2 – 4x + 3 equals 0, then what is the value of (x – 2)^2 ?   [#permalink] 10 Apr 2019, 17:54
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