3 root of 3 left parenthesis 3 root of x space minus space 1 divided by 3 root of x right parenthesis space equals 2 end root end root end root  then find value of   left parenthesis 3 root of x plus 1 divided by 3 root of x right parenthesis end root

Asked by Petulla Mishra | 30th Nov, 2014, 09:33: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n : 3 root of 3 open parentheses 3 root of x minus fraction numerator 1 over denominator 3 root of x end fraction close parentheses end root equals 2 C u b i n g space b o t h space t h e space s i d e s space o f space t h e space e q u a t i o n comma space w e space h a v e comma rightwards double arrow 3 open parentheses 3 root of x minus fraction numerator 1 over denominator 3 root of x end fraction close parentheses equals 2 cubed rightwards double arrow open parentheses 3 root of x minus fraction numerator 1 over denominator 3 root of x end fraction close parentheses equals 8 over 3... left parenthesis 1 right parenthesis C o n s i d e r space 3 root of x equals a space a n d space fraction numerator 1 over denominator 3 root of x end fraction equals b T h u s comma space e q u a t i o n space left parenthesis 1 right parenthesis space b e c o m e s comma space w e space h a v e comma open parentheses a minus b close parentheses equals 8 over 3... left parenthesis 2 right parenthesis W e space k n o w space t h a t space open parentheses a plus b close parentheses equals square root of open parentheses a minus b close parentheses squared plus 4 a b end root therefore E q u a t i o n space left parenthesis 2 right parenthesis space b e c o m e s comma space open parentheses a plus b close parentheses equals square root of open parentheses 8 over 3 close parentheses squared plus 4 cross times space 3 root of x cross times fraction numerator 1 over denominator 3 root of x end fraction end root rightwards double arrow open parentheses a plus b close parentheses equals square root of open parentheses 8 over 3 close parentheses squared plus 4 end root rightwards double arrow open parentheses a plus b close parentheses equals square root of 64 over 9 plus 4 end root rightwards double arrow open parentheses a plus b close parentheses equals square root of fraction numerator 64 plus 36 over denominator 9 end fraction end root rightwards double arrow open parentheses a plus b close parentheses equals square root of 100 over 9 end root rightwards double arrow open parentheses a plus b close parentheses equals 10 over 3 rightwards double arrow 3 root of x plus fraction numerator 1 over denominator 3 root of x end fraction equals 10 over 3

Answered by Vimala Ramamurthy | 1st Dec, 2014, 11:01: AM