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If x is positive and y is 1 more than the square of x, then

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If x is positive and y is 1 more than the square of x, then

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If x is positive and y is 1 more than the square of x, then what is the value of x in terms of y?

$$A.\ y^2\ -\ 1$$
$$B.\ y^2\ +\ 1$$
$$C.\ \sqrt{y}-\ 1$$
$$D.\ \sqrt{y\ -\ 1}$$
$$E.\ \sqrt{y\ +\ 1}$$

OA D

Source: Princeton Review

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Newbie | Next Rank: 10 Posts
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17 Aug 2018
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Hi,

It’s a straight forward question.

Given,

x is positive and y = x^2 + 1

y = x^2 +1

x^2 = y-1

x = sqrt(y-1)

So the answer is D.

OR

We can try numbers too.

If x = 1 then y = 2.

When we substitute y = 2 in the answer choices we should get “x” value as 1.

A. y^2 - 1 = 4 - 1 = 3. Eliminate.

B. y^2 + 1 = 4 + 1 = 5. Eliminate.

C. √(y)- 1 = √2 - 1 = not an integer. Eliminate.

D. √(y - 1) = √(2 - 1) = 1. Hold on.

E. √(y + 1) = √(2 + 1) = 3. Eliminate.

So the answer is D.

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BTGmoderatorDC wrote:
If x is positive and y is 1 more than the square of x, then what is the value of x in terms of y?

$$A.\ y^2\ -\ 1$$
$$B.\ y^2\ +\ 1$$
$$C.\ \sqrt{y}-\ 1$$
$$D.\ \sqrt{y\ -\ 1}$$
$$E.\ \sqrt{y\ +\ 1}$$
We can create the equation:

y = 1 + x^2

y - 1 = x^2

√(y - 1) = x

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

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