\(\displaystyle \text{Doesn't }\sqrt{1+\frac{2}{y^6}}\,\text{ evaluate to: }\,1 +\frac{4}{y^4}\:?\)
bcddd214 said:Brain fart,,,
doesn't ?(1+2/y^6) evaluate to 1+4/y^4? No
Next time, check these silly things yourself:bcddd214 said:Brain fart,,,
doesn't ?(1+2/y^6) evaluate to 1+4/y^4?
No.bcddd214 said:I apologize
doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?.
JeffM said:No.bcddd214 said:doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?
Actually, the correct answer to bcddd214's question above is "yes". :lol:
bcddd214 said:doesn't ?(1+ 4/y^6) evaluate to 1 + 2/y^4?
Please note that I removed the unneccesary grouping symbols from the first expression above.
mmm4444bot said:bcddd214 said:doesn't ?(1+ 4/y^6) evaluate to 1 + 2/y^4?
Please note that I removed the unneccesary grouping symbols from the first expression above.
We cannot evaluate sqrt(1 + 4/y^6) without knowing the value of y. I think that you're trying to ask about simplifying, instead.
So, yes, the expression sqrt(1 + 4/y^6) does not simplify to 1 + 2/y^4.
mmm4444bot said:
JeffM said:No.bcddd214 said:doesn't ?(1+(4/y^6)) evaluate to 1+2/y^4?
Actually, the correct answer to bcddd214's question above is "yes". :lol:
You are the mathematician, but may a wannabe historian present a possible counter-example a la mode du bon Denis.
Let's try y = 2.
(1 + (4/y[sup:3ud5rmel]6[/sup:3ud5rmel]))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (4/2[sup:3ud5rmel]6[/sup:3ud5rmel]))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (4/64))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = (1 + (1/16))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = sqrt(17) / 4.
1 + (2/y[sup:3ud5rmel]4[/sup:3ud5rmel]) = 1 + (2/16) = 1 + (1/8) = 9/8.
But (9/8)[sup:3ud5rmel]2[/sup:3ud5rmel] = 81/64 = 5.0625/4.
My problem is seeing how 5.06252[sup:3ud5rmel]2[/sup:3ud5rmel] > 25 = 17.
Of course, I admittedly am frequently in error, and arithmetic is not my forte, but I would love to know how you demonstrate that (1 + (4/y^6))[sup:3ud5rmel]1/2[/sup:3ud5rmel] = 1 + (2/y[sup:3ud5rmel]4[/sup:3ud5rmel])
PS I have this horrible feeling I am going to look extremely foolish before this is all over. Such as, you were teasing me and I was too literal-minded to twig, or else that devil Alzheimers has indeed caught up with me (which my newly acquired 18-year old wife keeps assuring me is the case as she hands me the power of attorney papers to sign).
bcddd214 said:The reason I 'thought' it did was because it looked pretty
Just as in life, looks can be deceiving. Don't be fooled by every pretty expression that crosses your path.
I plugged in evalf(sqrt(1+(4/y^6))); and it spit out the identical equation hinting that it could not be done.
That's because EVALF() is Maple's command for "evaluate the expression to a floating point number". You cannot get a Real number for this expression without first knowing a number that symbol y represents.
If you do not have any values for the symbol y, then the expression remains symbolic.
Another note about terminology: we don't call sqrt(1 + 4/y^6) an equation; it's called an expression. Equations always contain an equals sign.
You got me right between the eyes.mmm4444bot said:
Yeah, I was joshin' Jeff.
bcddd214 did not ask, "Does [this] evaluate to [that]".
They asked, "Does not [this] evaluate to [that]".
It does not, so the answer is "yes".
(I hope you're smiling right now.)
...you asked for it: you were leading with your noseJeffM said:You got me right between the eyes.