If (2x - 3)^(1/2) = x - 3, then what is the value of x ?

Question

If  \sqrt{2x-3}=x-3 , then what is the value of x ?

A. 1

B. 2

C. 3

D. 4

E. 6

Kinshook · Answer

Asked: If  \sqrt{2x-3}=x-3 , then what is the value of x ?

2x -3 >=0
x >=1.5

2x-3 = (x-3)^2
2x -3=x^2-6x+9
x^2-8x+12=0
(x-6)(x-2)=0

x = {2,6}
If x=2;  \sqrt{1}=-1 
If x=6;  \sqrt{9}=3

IMO E

Akp880 · Answer

Given  \sqrt{2x-3}=x-3

which means 2x-3 >=0 and x-3>=0
i.e x>=3/2 and x>=3
 x>=3 is the necessary condition

now squaring both sides of given equation

2x-3=(x-3)^2
x^2-8x+12=0
(x-6)(x-2)=0

x=6 (as x can't be less than 3)

Hence E is the correct answer IMO

MathRevolution · Answer

One way is to square both sides and solve 'x'.

But the quickest way will be to insert the options and check.

Option A: x = 1 => LHS (Square root negative -   NOT Possible  )

Option B: x = 2 => LHS ( \sqrt{4 - 3} = \sqrt{1}  = 1) and RHS (2 - 3 = -1) -   NOT Equal

Option C: x = 3 => LHS ( \sqrt{6 - 3} = \sqrt{3}  = 1.732) and RHS (3 - 3 = 0) -   NOT Equal

Option D: x = 4 => LHS ( \sqrt{8 - 3} = \sqrt{5}  = 2.xx) and RHS (4 - 3 = 1) -   NOT Equal

Option E: x = 6 => LHS ( \sqrt{12 - 3} = \sqrt{9}  = 3) and RHS (6 - 3 = 3) -   Equal - Answer

Answer E

ScottTargetTestPrep · Answer

Solution:

Since a square root can never be negative, we see that x can’t be 1 or 2 (notice that the right hand side will be -2 and -1, respectively).

If x = 3, the left hand side is √3 while the right hand side is 0.

If x = 4, the left hand side is √5 while the right hand side is 1.

If x = 6, the left hand side is √9 = 3 and the right hand side is 3. Since both sides of the equation are 3, x = 6.

Alternate Solution:

Let’s square both sides of the given equation and then solve for x:

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

0 = x^2 - 8x + 12

0 = (x - 6)(x - 2)

We see that x can equal either 6 or 2.

Because this is a square root equation, we need to test each possible solution, in case there is an extraneous solution. We see that x = 6 works in the original equation, but x = 2 does not because we would have √(4 - 3) = 2 - 3, which would yield the false statement 1 = -1.

Answer: E

Basshead · Answer

Fastest way is to plug in the answer and check:

A. left hand side is negative

B. left hand side is negative

C. left hand side is 1.7 = right hand side is 0

D. left hand side is sqrt5 = right hand side is 1

E. 3 = 3 . Answer is E.

bumpbot · Answer

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If (2x - 3)^(1/2) = x - 3, then what is the value of x ?

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If (2x - 3)^(1/2) = x - 3, then what is the value of x ?

Prep Toolkit

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