🚀 go-pugleaf

In article <33017.2B3AC0F2@puddle.fidonet.org>, Lloyd.Johnston@p0.f45.n342.z1.fidonet.org (Lloyd Johnston) writes:
|> EG> Here is a problem I don't really understand how the result is
|> EG> reached.
|> EG> Prob.   sqrt(y) + sqrt(y+5) = 5
|> EG> Ans.  y=4
|> EG> I see that if you just pop in 4  you get 2+3=5.

The solution to an equation is the set of values that y can be substituted
with to make the STATEMENT sqrt(y) + sqrt(y+5) = 5 TRUE.


|> however I thought
|> EG> that sqrt(y+5) was the same as sqrt(y) + sqrt(5) giving y=10

SUPPOSE that sqrt(y+5) = sqrt(y) + sqrt(5). Then we can claim
sqrt(1 + 5) = sqrt 1 + sqrt 5 = 1 + sqrt 5 = sqrt 6. But we KNOW that
sqrt 6 is NOT 1 + sqrt 5. So we have found that sqrt(y+5) is NOT equal
to sqrt(y) + sqrt(5), at least, not in GENERAL. 

But you can see that sqrt(y+5) = sqrt(y) + sqrt(5) is an EQUATION.
What is the solution to the equation?

Is the solution the set of nonnegative real numbers?

Note: sqrt(5y) = sqrt 5 x sqrt y for all nonnegative y.

-- 

Henry Choy
choy@cs.usask.ca

"The Log Song", from Ren & Stimpy
 
   "What rolls down stairs alone or in pairs
    Rolls over your neighbor's dog?
    What's great for a snack and fits on your back?
    It's Log, Log, Log!
 
    It's Log, Log, it's big, it's heavy, it's wood.
    It's Log, Log, it's better than bad, it's good!
    Everyone wants a log! You're gonna love it, Log!
    Come on and get your log! Everyone needs a Log!"


"Math is tough!"

      -- Barbie