CBSE Class 10 Answered

let a,b,c,k be rational number such that k is not a perfect cube if a+6k1/3 +ck2/3=0 then prove that a=b=c=0.

Asked by | 13 Jul, 2014, 08:06: PM

Expert Answer

$S q u a r i n g space e q u a t i o n space left parenthesis 5 right parenthesis comma space w e space h a v e a squared b squared equals c to the power of 4 k squared rightwards double arrow a squared open parentheses a squared close parentheses equals c to the power of 4 k squared rightwards double arrow a squared open parentheses a c close parentheses equals c to the power of 4 k squared rightwards double arrow a cubed c minus c to the power of 4 k squared equals 0 rightwards double arrow c open parentheses a cubed minus k squared c cubed close parentheses equals 0 rightwards double arrow c equals 0 space o r space a cubed minus k squared c cubed equals 0 rightwards double arrow c equals 0 space o r space a cubed equals k squared c cubed rightwards double arrow c equals 0 space o r fraction numerator space a cubed over denominator c cubed end fraction equals k squared rightwards double arrow c equals 0 space o r space k squared equals open parentheses a over c close parentheses cubed rightwards double arrow c equals 0 space o r space k to the power of 2 over 3 end exponent equals open parentheses a over c close parentheses B u t space k space i s space i r r a t i o n a l space a n d space h e n c e space w e space h a v e comma space a cubed minus k squared c cubed not equal to 0 rightwards double arrow c equals 0 S i n c e space b squared equals a c comma space w e space h a v e comma space b equals 0 b equals 0 space a n d space c equals 0 space a n d space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma space a equals 0 T h u s comma space w e space h a v e comma space a equals 0 comma space b equals 0 space a n d space c equals 0$