PROVE THAT:(i)p x squared minus p x plus q equals 0 space i f. space x equals fraction numerator square root of p plus 2 q end root space plus square root of p minus 2 q end root over denominator square root of p plus 2 q end root minus square root of p minus 2 q end root end fraction
(ii)open parentheses 33 over 243 close parentheses to the power of minus 4 divided by 5 end exponentequals 81 over 16

Asked by araima2001 | 5th Sep, 2014, 07:37: 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 : x equals fraction numerator square root of p plus 2 q end root plus square root of p minus 2 q end root over denominator square root of p plus 2 q end root minus square root of p minus 2 q end root end fraction A p p l y i n g space c o m p o n e n d o space a n d space d i v i d e n d o comma space w e space h a v e comma fraction numerator x plus 1 over denominator x minus 1 end fraction equals fraction numerator square root of p plus 2 q end root plus square root of p minus 2 q end root plus square root of p plus 2 q end root minus square root of p minus 2 q end root over denominator square root of p plus 2 q end root plus square root of p minus 2 q end root minus square root of p plus 2 q end root plus square root of p minus 2 q end root end fraction space space space space space space space space space space equals fraction numerator 2 square root of p plus 2 q end root over denominator 2 square root of p minus 2 q end root end fraction space space space space space space space space space space equals fraction numerator square root of p plus 2 q end root over denominator square root of p minus 2 q end root end fraction S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma open parentheses fraction numerator x plus 1 over denominator x minus 1 end fraction close parentheses squared equals fraction numerator p plus 2 q over denominator p minus 2 q end fraction rightwards double arrow fraction numerator x squared plus 1 plus 2 x over denominator x squared plus 1 minus 2 x end fraction equals fraction numerator p plus 2 q over denominator p minus 2 q end fraction rightwards double arrow open parentheses x squared plus 1 plus 2 x close parentheses open parentheses p minus 2 q close parentheses equals open parentheses x squared plus 1 minus 2 x close parentheses open parentheses p plus 2 q close parentheses rightwards double arrow p x squared minus 2 q x squared plus p minus 2 q plus 2 x p minus 4 x q equals p x squared plus 2 q x squared plus p plus 2 q minus 2 x p minus 4 x q rightwards double arrow 4 q x squared plus 4 x p minus 4 q equals 0 rightwards double arrow q x squared plus x p minus q equals 0  left parenthesis i i right parenthesis
Please check the question in sub part (ii)

Answered by Vimala Ramamurthy | 8th Sep, 2014, 10:20: AM

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