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# If root{3-2x} = root(2x) +1, then 4x^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 44286
Re: If root{3-2x} = root(2x) +1, then 4x^2 = [#permalink]

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30 May 2015, 04:43
reto wrote:
Bunuel wrote:
If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

Diagnostic Test
Question: 16
Page: 22
Difficulty: 600

Why is this question categorized as difficulty 700 above and 600 in the question steam? What's the actual difficulty?

If you square the expression $$\sqrt{2x} +1$$ and there are NO paranthesis, why is it not correct to square each term seperately to get 2x + 1?

Thank you so much

1. 600 difficulty was given when posted. 700 difficulty is based on users' answers on the question.
2. (a + b)^2 generally does not equal to a^2 + b^2. I'ts pretty basic actually.
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Re: If root{3-2x} = root(2x) +1, then 4x^2 = [#permalink]

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30 May 2015, 05:04
Bunuel wrote:
reto wrote:
Bunuel wrote:
If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

Diagnostic Test
Question: 16
Page: 22
Difficulty: 600

Why is this question categorized as difficulty 700 above and 600 in the question steam? What's the actual difficulty?

If you square the expression $$\sqrt{2x} +1$$ and there are NO paranthesis, why is it not correct to square each term seperately to get 2x + 1?

Thank you so much

1. 600 difficulty was given when posted. 700 difficulty is based on users' answers on the question.
2. (a + b)^2 generally does not equal to a^2 + b^2. I'ts pretty basic actually.

Thanks. Thats what I meant in the question there are no paranthesis, but when you squared it in your solution, you gave the expression extra paranthesis - why? I know it's not the same. But I don't understand why you completed it when squaring...
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Math Expert
Joined: 02 Sep 2009
Posts: 44286
Re: If root{3-2x} = root(2x) +1, then 4x^2 = [#permalink]

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30 May 2015, 05:21
1
KUDOS
Expert's post
reto wrote:
Thanks. Thats what I meant in the question there are no paranthesis, but when you squared it in your solution, you gave the expression extra paranthesis - why? I know it's not the same. But I don't understand why you completed it when squaring...

Squaring means multiplying by the same number, so when you square a + b, you get (a + b)(a + b) = (a + b)^2.

I'd advice to brush up fundamentals before practicing questions, especially, hard ones.
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Re: If root{3-2x} = root(2x) +1, then 4x^2 = [#permalink]

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20 Mar 2016, 18:25
Bunuel wrote:
If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

Diagnostic Test
Question: 16
Page: 22
Difficulty: 600

sqrt(3-2x)-1 = sqrt(2x) | square everything
2x = 3-2x - 2*sqrt(3-2x)+1
2x=4 - 2x - 2*sqrt(3-2x)
4-4x=2*sqrt(3-2x) | square everything again
16+16x^2 -32x = 12 - 8x | add 8x to both sides, subtract 12 from both sides
16x^2 - 24x +4 = 0 | divide by 4
4x^2 -6x +1 = 0 | add 6x to both sides and subtract 1:
4x^2 = 6x-1

E
Director
Joined: 17 Dec 2012
Posts: 635
Location: India
Re: If root{3-2x} = root(2x) +1, then 4x^2 = [#permalink]

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08 Mar 2018, 18:48
Bunuel wrote:
If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

Diagnostic Test
Question: 16
Page: 22
Difficulty: 600

Main Idea:While simplifying keep the more complex root expression alone on one side and simplify.

Details: sqrt(3-2x)=sqrt(2) +1.

Squaring on both sides: 3-2x=2x+1+2*sqrt(2x)

Simplifying we get (4x)^2 = 6x-1

Hence E.
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Standardized Approaches

Re: If root{3-2x} = root(2x) +1, then 4x^2 =   [#permalink] 08 Mar 2018, 18:48

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