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\sqrt x^4 + 6x^2

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\sqrt x^4 + 6x^2 [#permalink]  17 Mar 2018, 03:21
Expert's post
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Question Stats:

55% (00:25) correct 45% (02:21) wrong based on 20 sessions
 Quantity A Quantity B $$\sqrt{x^4 + 6x^2 + 9}$$ $$x^2 + 3$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: \sqrt x^4 + 6x^2 [#permalink]  21 Mar 2018, 22:15
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Since quantity $$A$$ is under square root it would be easier to simplify if that square root could be removed
Hence, square both sides
Qty A = $$x^4 + 6x^2 + 9$$
Qty B = $$(x^2 +3)^2$$
Qty B can be squared by using the formula $$(a+b)^2 = a^2 + b^2 + 2ab = x^4 +6x^2 + 9$$
Qty A = Qty B
option c
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Re: \sqrt x^4 + 6x^2 [#permalink]  22 Nov 2018, 14:42
The answer is wrong. the root of square can be + or -. the answer can be -x^2-3 which will be less than x^2+3. D is the correct answer
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Re: \sqrt x^4 + 6x^2 [#permalink]  22 Nov 2018, 22:49
Expert's post
Drow198 wrote:
The answer is wrong. the root of square can be + or -. the answer can be -x^2-3 which will be less than x^2+3. D is the correct answer

 Quantity A Quantity B $$\sqrt{x^4 + 6x^2 + 9}$$ $$x^2 + 3$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Hi, it is correct.

$$\sqrt{x^4 + 6x^2 + 9}=\sqrt{(x^2+3)^2}$$....
Always remember that the square root is always positive..

this means
$$x^2=25$$ means x=5 or x=-5
whereas $$\sqrt{25}$$ can only be 5 and not -5.

thus, $$A=\sqrt{x^4 + 6x^2 + 9}=\sqrt{(x^2+3)^2}=x^2+3=B$$

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: \sqrt x^4 + 6x^2   [#permalink] 22 Nov 2018, 22:49
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