Today one of our interns asked for some help with an algebra problem, so I said “sure, send it to me.” It turned out to be a little tougher than I thought. I had to reach way back into the memory banks and even look up the quadratic formula.

It took me about 20 minutes to figure it out, but it was pretty satisfying to get the right answer. Here is is…

**(click for a larger version) **

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Or you can plug it into your TI 89 calculator and it will solve it for you…. Kids have it easy these days.

Those kids with their fancy adding machines and indoor plumbing.

Wow. What a brain teaser, huh ? I needed that last night to cheer me up (wink, wink). Can’t say I didn’t have to think about it though. But it didn’t take 20 minutes. Plus, your solution looks way more complicated than mine. Must be the difference between Texas algebra and what they taught us in Germany…

(4x+1)exp1/2 – (x-2)exp1/2 = 3

(4x+1)exp1/2 = 3 + (x-2)exp1/2

4x + 1 = 9 + 6* (x-2)exp1/2 + x – 2

3x + 3 = 9 + 6*(x-2)exp1/2

x = 2 + 2*(x-2)exp1/2

(x-2)exp1/2 = 4*(x-2)

xexp2 – 4x + 4 = 4x – 8

xexp2 + 4 = 4x – 8

xexp2 – 4x + 12 = 0

(x-2)(x-6) = 0

from which follow either x=2 or x=6

Arne & Kevin,

Your solutions look much more complicated than it should be:

(4x+1)^1/2 – (x-2)^1/2 = 3

aka, eq.1 – eq.2 = 3

have 3-4 beers…

eq.2, if x = 2, then eq.2 goes away.

eq.1, 4(2) + 1 = 9, yep, so x=2.

Hey, let’s try 6 because 2×3 = 6, and if x = 6, eq.1 and eq.2 have easy numbers to sqrt.

… hmmm it works. Hic!

more beers.

It also helps when two smart people solved it so you can cheat off them in case the above fails.

It took us both 8 steps to get the to quadratic equation. You just solved the quadratic by observation and I used the quadratic formula.

But I didn’t have to go look up some formula.

Paper is for wimps