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 2 years ago
is my working correct? i need to find which number is bigger. i concluded that 2*sqrt38 is bigger of the two since 38^2 = 1444
 2 years ago
is my working correct? i need to find which number is bigger. i concluded that 2*sqrt38 is bigger of the two since 38^2 = 1444

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asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1yes  correct again. BTW: you can make use of this fact:\[a^2\gt a^21\]\[\therefore a^2\gt (a+1)(a1)\]In this case a=38 so you know that:\[38^2\gt (38+1)(381)\]

tomiko
 2 years ago
Best ResponseYou've already chosen the best response.2how did you just decide a = 38? @asnaseer

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1in your last step you had:\[38^2?39\times37\]

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1so can conclude ? is ">" without actually evaluating \(38^2\)

tomiko
 2 years ago
Best ResponseYou've already chosen the best response.2but 38^2 is "a" but 39 x 37 is not = (a+1)(a1) so how can you compare that way?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1no, a=38, remember the identity I showed was:\[a^2\gt (a+1)(a1)\]so, if a=38 we get:\[38^2\gt(38+1)(381)\]\[\therefore 38^2\gt39\times37\]

tomiko
 2 years ago
Best ResponseYou've already chosen the best response.2wow!! i see it now. where did you know this. i never came across this before?

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1nor did I  I just suddenly "spotted" the pattern  that is one of the beauty of maths, you never know what subtleties you will discover. :)
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