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# If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll

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Joined: 12 Sep 2015
Posts: 2710
Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll  [#permalink]

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11 Aug 2017, 14:02
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Bunuel wrote:

Tough and Tricky questions: Algebra.

If $$\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}$$, then x could be equal to which of the following?

A. -1
B. 0
C. 1
D. 4
E. cannot be determined.

Kudos for a correct solution.

As has already been demonstrated, the fastest solution is to plug in each answer choice. This allows us to solve the question in well under a minute.
That said, we can also solve the equation algebraically.

For equations involving square roots, we must make sure we test for extraneous roots (more in the video below).

Given: $$\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}$$

Square both sides to get: 4 + x^(1/2) = x + 2
Subtract 4 from both sides: x^(1/2) = x - 2
Square both sides: x = (x - 2)²
Expand: x = x² - 4x + 4
Subtract x from both sides: 0 = x² - 5x + 4
Factor: 0 = (x - 1)(x - 4)
So, EITHER x = 1 OR x = 4

IMPORTANT: Now plug the solutions into the original equation to check for extraneous roots.

Try x = 1
Given:$$\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}$$
Replace x with 1 to get: $$\sqrt{4 + 1^{\frac{1}{2}}} =\sqrt{1 + 2}$$
Simplify: $$\sqrt{5} =\sqrt{3}$$
Doesn't work.
ELIMINATE x = 1

Try x = 4
Given:$$\sqrt{4 + x^{\frac{1}{2}}} =\sqrt{x + 2}$$
Replace x with 4 to get: $$\sqrt{4 + 4^{\frac{1}{2}}} =\sqrt{4 + 2}$$
Simplify: $$\sqrt{4 + 2} =\sqrt{4 + 2}$$
Simplify: $$\sqrt{6} =\sqrt{6}$$
WORKS!!

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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll  [#permalink]

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11 Aug 2018, 14:26
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Re: If √(4 + x^1/2) =√(x + 2) , then x could be equal to which of the foll &nbs [#permalink] 11 Aug 2018, 14:26

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