Permutations and Combinations

Permutations and Combinations

Question

If a, b, c are in A.P. then prove that left parenthesis straight a minus straight c right parenthesis squared space equals space 4 left parenthesis straight b squared minus ac right parenthesis

Answer

Since a, b, c are in A.P.

∴           b - a = c - b      or    2b = a + c        or      straight b space equals space fraction numerator straight a plus straight c over denominator 2 end fraction                    ...(i)
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#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...')
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#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>
                                                                                            [ By using (i)]
if           straight a squared plus straight c squared minus 2 ac space equals space left parenthesis straight a plus straight c right parenthesis squared minus 4 ac  or  if  straight a squared plus straight c squared minus 2 ac space equals space straight a squared plus straight c squared plus 2 ac minus 4 ac
if              - 2ac = -2ac which is true

∴                left parenthesis straight a minus straight c right parenthesis squared space equals space 4 left parenthesis straight b squared minus ac right parenthesis

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