How do you solve #a^2=4a#?

1 Answer
Feb 14, 2017

Answer:

See below.

Explanation:

With quite some care!

Good practise is to re-write it as follows:

#a^2 = 4 a #

#implies a^2 - 4 a = 0#

And then factor it:

#implies a(a - 4) = 0#

So now you know that you have two solutions, ie #a = 0 # and #a = 4#.

The temptation here, which exists all the way up the maths tree (to my branch, at least!), is to cancel out the #a# terms, ie to say that #a^2 = 4 a implies a = 4#.

But that just throws away a solution :(

Zero is every bit as scarey as infinity, perhaps even scarier!