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Femme_physics
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If
xy2 = ab2
Does that mean automatically that xy = ab?
xy2 = ab2
Does that mean automatically that xy = ab?
Femme_physics,Femme_physics said:If
xy2 = ab2
Does that mean automatically that xy = ab?
I did not assume the OP meant {if [itex] (xy)^2 = (ab)^2[/itex], does [itex] xy = ab[/itex]. I approached it as written {if [itex] xy^2 = ab^2 [/itex] does [itex] xy = ab[/itex]} which is false. Without proving it, by testing empirically, it becomes obvious it is false.Alex1812 said:Assuming you mean (xy)^2 = (ab)^2, xy does not neccesarily equal ab:
sqrt[(xy)^2] = sqrt[(ab)^2]
then
(+/-)xy = (+/-)ab
which is true for only two out of four cases:
+xy=+ab
-xy=-ab
But, you wind up with problems when -xy = +ab and +xy=-ab.
not true if y =0 and x = 0Alex1812 said:if (xy^2)=(ab^2)
then (x/a) = (b^2/y^2)
if xy=ab
then (x/a)=(b/y)
Then the original statement is true only iff (b/y)=(b^2/y^2)=((b/y)^2) which, as previously pointed out, is only true iff b=y.
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No, xy does not necessarily equal ab. This is because the variable y can have any value, which means that y^2 will also have any value. Therefore, xy can be equal to ab^2 or ab^3 or any other combination depending on the value of y.
No, you cannot simplify xy^2 = ab^2 to xy = ab. This is because when simplifying equations, you must apply the same operation to both sides of the equation. In this case, the exponent of y is different on both sides, so you cannot simply cancel them out.
The relationship between xy^2 and ab^2 is that they are both equal to each other. This is because the equation xy^2 = ab^2 means that both expressions are equivalent and have the same value. However, this does not mean that xy is equal to ab, as explained in the first question.
Yes, xy^2 = ab^2 can be solved for either x or y. However, the solution will be in terms of the other variable. For example, if you solve for x, the equation will become x = ab^2/y^2. Similarly, if you solve for y, it will become y = √(ab^2/x).
The main difference between xy^2 = ab^2 and xy = ab is that the first equation includes an exponent, while the second one does not. This means that the first equation has two variables, x and y, raised to different powers, while the second equation has only two variables, x and y, with no exponents. As a result, the solutions for both equations will be different.