For the equation y= x2+2 x2−1 , express x in terms of y and determine the values of y for which x is real.

y can take on values in:

Step-by-step explanation:

Hopefully this is the right equation:

.

Multiply both sides by :

Distribute:

Put x terms on one side together and non-x terms on opposite side.

Add y on both sides

and subtract x^2 on both sides:

Factor:

Divide both sides by (y-1):

Now square root both sides:

y cannot be 1 because we don't want to divide by 0.

Now we also need to find when (y+2)/(y-1) is positive or zero because we can't square root negative values if we intend to have just real solutions.

The fraction is zero when y=-2 because that will give us 0 on top.

I'm going to draw a number line and test which intervals gives us positive values for our expression under the square root.

--------(-2)-------(1)----------

Plugging in -3 gives us (-3+2)/(-3-1)=(-1)/(-4)=1/4 so anything before -2 works.

Let's try 0: (0+2)/(0-1)=-2 so nothing between -2 and 1 will work.

Let's try it for 2: (2+2)/(2-1)=4/1=4 so anything after 1 will work.

So y can take on values in:

the correct answer is 828.07

2160ft3

step-by-step explanation: