Question
Sat October 13, 2012 By: Prashanth Balasubramaniam
 

if x=3+3root2 ,find the value of x2+1/x2

Expert Reply
Sat October 13, 2012
Answer : Given :  x=3+3(2)1/2
To find the value of x2+1/(x2)
 
x2 = (3+3(2)1/2)    { (a+b)2 = a2 + b2 + 2ab)}
     = 32 + (3(2)1/2) + 2 (3)(3 (21/2))
     = 9 + 9(2) + 18 (21/2
 x2  = 27 + 18 (21/2)......................(1)
 
according to the question 
=> x2+1/(x2
=> 27 + 18 (21/2) + 1/ ( 27 + 18 (21/2))    {using eq1}
=> ( (27 + 18 (21/2))2+1 ) / 27 + 18 (21/2))
 =>( 729 + 648 + 2(27)(18(21/2)) +1) / 27 + 18 (21/2))  { applying (a+b)2 = a2+b2+ 2ab}
=>  (1378 + 972 (21/2) ) / ( 27 + 18 (21/2))
rationliasing the equation, we get
=> [(1378 + 972 (21/2) )( 27 - 18 (21/2)) ]/ [ 272-(18 (21/2))2 ]            { using (a+b)(a-b)= a2 -b2}
= [37206 - 34992 + 24804(21/2) ] /81
= [2214 +24804(21/2) ] / 81 Answer
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