Question
Mon March 16, 2015 By: Renuka Reddy

list all the identities of Langrange
 
can we solve this .......... using his identities
   

Expert Reply
Vimala Ramamurthy
Tue March 17, 2015
L a r a n g e apostrophe s space I d e n t i t y colon open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar equals open vertical bar a with rightwards arrow on top close vertical bar squared open vertical bar b with rightwards arrow on top close vertical bar squared minus open parentheses a with rightwards arrow on top. b with rightwards arrow on top close parentheses squared Q u e s t i o n space s h o u l d space b e I f space open vertical bar a with rightwards arrow on top close vertical bar equals square root of 26 comma space open vertical bar b with rightwards arrow on top close vertical bar equals 7 space a n d space open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar equals 35 comma space f i n d space a with rightwards arrow on top. b with rightwards arrow on top. S o l u t i o n colon U sin g space L A G R A N G E apostrophe S space I D E N T I T Y comma space w e space h a v e comma open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar squared equals open vertical bar a with rightwards arrow on top close vertical bar squared open vertical bar b with rightwards arrow on top close vertical bar squared minus open parentheses a with rightwards arrow on top. b with rightwards arrow on top close parentheses squared rightwards double arrow open parentheses a with rightwards arrow on top. b with rightwards arrow on top close parentheses squared equals open vertical bar a with rightwards arrow on top close vertical bar squared open vertical bar b with rightwards arrow on top close vertical bar squared minus open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar squared... left parenthesis 1 right parenthesis  S i n c e space open vertical bar a with rightwards arrow on top close vertical bar equals square root of 26 comma space open vertical bar b with rightwards arrow on top close vertical bar equals 7 comma space open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar equals square root of 26 cross times 7 semicolon space open square brackets open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar close square brackets squared equals open square brackets square root of 26 cross times 7 close square brackets squared equals 26 cross times 7 squared equals 26 cross times 49 equals 1274  F r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma open parentheses a with rightwards arrow on top. b with rightwards arrow on top close parentheses squared equals open vertical bar a with rightwards arrow on top close vertical bar squared open vertical bar b with rightwards arrow on top close vertical bar squared minus open vertical bar a with rightwards arrow on top cross times b with rightwards arrow on top close vertical bar squared space space space space space space space space space equals 1274 minus 35 squared space space space space space space space space space equals 49 a with rightwards arrow on top. b with rightwards arrow on top equals square root of 49 equals 7 P l e a s e space c h e c k space y o u r space q u e s t i o n.
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