Permutations and Combinations

Question

The A.M. between two positive numbers is 34 and their GM. is 16. Find the numbers.

Answer

Let a and b be two numbers
 A.M. = 34 $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ ...(i)
 G.M. = 16 $rightwards double arrow space square root of ab space equals space 16 space space space space rightwards double arrow space ab space equals space 256$ ...(ii)
From (i), b = 68 - a
Using in (ii), we get
 a(68 - a) = 256 $rightwards double arrow$ $68 straight a minus straight a squared space equals space 256$
$rightwards double arrow$ $straight a squared minus 68 straight a plus 256 equals 0$ $rightwards double arrow$ $straight a squared minus 64 straight a minus 4 straight a plus 256 equals 0$
$rightwards double arrow$ a(a - 64) - 4 (a - 64) = 0 $rightwards double arrow$ (a - 64) (a - 4) = 0
$rightwards double arrow$ a = 4, 64
When a = 4, b = 68 - 4 = 64
and a = 64, b = 68 - 64 = 4