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

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In summary, when solving for y in an equation with a square root, both the positive and negative roots must be considered. This is because the even root of a number is defined to be the positive number, but when solving for y, both the positive and negative roots can be solutions. Therefore, the plus/minus sign must be included when solving for y in an equation with a square root.
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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, [itex]\sqrt{1-x}[/itex] 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.
 
  • #3
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.
 

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

What is the value of x in the equation 16x-y^4=0?

The value of x cannot be determined from the given equation alone. Additional information or equations are needed to solve for the value of x.

Can the equation be solved for y?

Yes, the equation can be solved for y. Rearranging the terms, we get y^4=16x, and taking the fourth root of both sides, we get y=±√(16x). The solution for y will have both positive and negative values.

Is this equation linear or quadratic?

This equation is neither linear nor quadratic. It is a quartic equation, which means it has a degree of 4. This is because the variable y is raised to the fourth power.

Can you graph this equation?

Yes, this equation can be graphed on a coordinate plane. The resulting graph will be a curve, not a straight line, since it is a quartic equation. The shape of the curve will depend on the value of x.

How many solutions does this equation have?

This equation has an infinite number of solutions. Since it is a quartic equation, it will have four complex solutions. However, for any given value of x, there will be two real solutions for y, one positive and one negative.

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