Dave Posted August 21, 2003 Share Posted August 21, 2003 I'm bored, so here's a nice piece of maths: Simplify sqrt(2 + sqrt(3)) - sqrt(2- sqrt(3)). A few of you may have already seen this - if so, don't spoil it for the others. It's not supposed to be hard, but it's fairly nice. Link to comment Share on other sites More sharing options...
YT2095 Posted August 22, 2003 Share Posted August 22, 2003 never seen it, but at 1`st glance looks a bit self defeating, and so I`de guess at Zero? I`ll check when I get more time though Link to comment Share on other sites More sharing options...
Dave Posted August 22, 2003 Author Share Posted August 22, 2003 Obviously not zero. first term clearly != second term. Hint: put it in your calculator, then try and simplify. (yes, it's cheating ) Link to comment Share on other sites More sharing options...
YT2095 Posted August 22, 2003 Share Posted August 22, 2003 surely if the 1`st term = X and the second = X also then a subtraction of X-X=0 regardless of what X might equal after the 1`st term? (still haven`t grabbed ma calc yet tho ) Link to comment Share on other sites More sharing options...
YT2095 Posted August 22, 2003 Share Posted August 22, 2003 Oooops MY bad! I didn`t see the `-` in the second term were used + in the 1`st.... term 1 and 2 looked the same.... forgive my oversight Link to comment Share on other sites More sharing options...
Dave Posted August 22, 2003 Author Share Posted August 22, 2003 Yup, they're two different terms. Link to comment Share on other sites More sharing options...
quack Posted August 22, 2003 Share Posted August 22, 2003 I used my calculator and got square root of 2 (actually 1.4 etc.). What is the reasoning behind it? Link to comment Share on other sites More sharing options...
Dave Posted August 23, 2003 Author Share Posted August 23, 2003 I'll tell you all a bit later on if you haven't got it by then Link to comment Share on other sites More sharing options...
Dave Posted August 24, 2003 Author Share Posted August 24, 2003 Okay, I can't be bothered waiting for someone to reply, so here's the answer. Let x = sqrt(2 + sqrt(3)) - sqrt(2- sqrt(3)) This means x^2 = 4 - 2*sqrt((2+sqrt(3))(2-sqrt(3)) = 4 - 2 * sqrt(1) = 2 Therefore x = sqrt(2) There we go. Ta da etc. Link to comment Share on other sites More sharing options...
cHIs- Posted August 24, 2003 Share Posted August 24, 2003 dave said in post #1 :I'm bored, so here's a nice piece of maths: Simplify sqrt(2 + sqrt(3)) - sqrt(2- sqrt(3)). A few of you may have already seen this - if so, don't spoil it for the others. It's not supposed to be hard, but it's fairly nice. WTF!? Link to comment Share on other sites More sharing options...
Dave Posted August 24, 2003 Author Share Posted August 24, 2003 ? There ain't nothin hard about it, it's just seeing a method. Link to comment Share on other sites More sharing options...
cHIs- Posted August 24, 2003 Share Posted August 24, 2003 its hard when your me Link to comment Share on other sites More sharing options...
Dave Posted August 24, 2003 Author Share Posted August 24, 2003 read up some more on algebra and it'll become a bit more apparent. Link to comment Share on other sites More sharing options...
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