tomiko 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

1. tomiko

attched is my working

2. jasonxx

seems correct

3. tomiko

thanks a lot!

4. jasonxx

(:

5. asnaseer

yes - correct again. BTW: you can make use of this fact:$a^2\gt a^2-1$$\therefore a^2\gt (a+1)(a-1)$In this case a=38 so you know that:$38^2\gt (38+1)(38-1)$

6. tomiko

how did you just decide a = 38? @asnaseer

7. asnaseer

in your last step you had:$38^2?39\times37$

8. asnaseer

so can conclude ? is ">" without actually evaluating $$38^2$$

9. tomiko

but 38^2 is "a" but 39 x 37 is not = (a+1)(a-1) so how can you compare that way?

10. asnaseer

no, a=38, remember the identity I showed was:$a^2\gt (a+1)(a-1)$so, if a=38 we get:$38^2\gt(38+1)(38-1)$$\therefore 38^2\gt39\times37$

11. tomiko

wow!! i see it now. where did you know this. i never came across this before?

12. asnaseer

nor did I - I just suddenly "spotted" the pattern - that is one of the beauty of maths, you never know what subtleties you will discover. :)

13. tomiko

thanks...

14. asnaseer

yw :)