Ok I'm a little confused with this: 16x-y^4=0

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The discussion centers on the equation 16x - y^4 = 0, with confusion regarding the inclusion of the plus/minus sign when solving for y. It is clarified that when solving for y from y = ±√(16x), the plus/minus indicates that both positive and negative roots are valid solutions, thus confirming it is not a function. In contrast, for y = √(1-x), the square root is defined as the positive root, but when solving for y, both positive and negative roots should be considered. The key takeaway is that the plus/minus sign is necessary when solving for y from an equation involving square roots, while the even root is conventionally taken as positive. Understanding when to apply the plus/minus sign is crucial for correctly interpreting solutions in equations.
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Ok I'm a little confused with this:

16x-y^4=0

When you solve for (y) you get: y= plus/minus 4th root(16x) right?
There for it isn't a function.

What about y=sq.rt.(1-x)? Does it have the plus/minus automatically? Do you only put the plus/minus sign if you solve for y?

I just don't get when you have to put the plus/minus in front of the sq.rt. Do you always have to put one there? or only if you solve for y, etc.?
 
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Well, the even root of a number is DEFINED to be the positive number.
That is, by definition, \sqrt{1-x} is a positive number.

When you solve for y, however, you must remember that not only do you have the positive, even root as a solution, but also the negative of that number.
 
Oh ok. So if they give you an equation that has no plus/minus infront of it, then the equation is POSITIVE. However, if you solve for y and get a sq.rt. then you must put the plus/minus sign right? Thanks.
 

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Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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