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ques 22

Asked by rbhatt16 20th October 2017, 10:03 AM
Answered by Expert
Answer:
begin mathsize 12px style F i r s t space E q u a t i o n space x squared minus 2 x plus A space equals space 0

r o o t s space o f space a b o v e space e q u a t i o n space fraction numerator 2 plus-or-minus square root of 4 minus 4 A end root over denominator 2 end fraction space equals space space 1 plus-or-minus square root of 1 minus A end root

H e n c e space alpha space equals space 1 minus square root of 1 minus A end root space space a n d space beta space equals space 1 plus square root of 1 minus A end root

S e c o n d space E q u a t i o n space x squared minus 18 x plus B space equals space 0

r o o t s space o f space s e c o n d space e q u a t i o n space fraction numerator 18 plus-or-minus square root of 324 minus 4 B end root over denominator 2 end fraction space equals space 9 plus-or-minus square root of 81 minus B end root

H e n c e space gamma space equals space 9 minus square root of 81 minus B space end root space a n d space delta space equals space 9 plus square root of 81 minus B end root

alpha comma space beta comma space gamma space a n d space delta space a r e space i n space A r i t h m a t i c space p r o g r e s s i o n

beta minus alpha space equals space d space equals space 2 square root of 1 minus A end root comma space w h e r e space d space i s space t h e space c o m m o n space d i f f e r e n c e

s i m i l a r l y space delta minus gamma space equals space d space equals space 2 square root of 81 minus B end root

h e n c e space 2 square root of 1 minus A end root space equals space 2 square root of 81 minus B end root comma space t h i s space g i v e s space B minus A space equals space 80

n o w space gamma minus beta space equals space d space equals space 9 minus square root of 81 minus B end root space minus 1 space minus space square root of 1 minus A end root space

2 square root of 1 minus A end root space equals space 8 minus 2 square root of 1 minus A end root space space space left parenthesis space t h i s space i s space o b t a i n e d space b y space s u b s t i t u t i n g space d space equals space 2 square root of 1 minus A space end root a n d space B space equals space 80 plus A space right parenthesis

h e n c e space square root of 1 minus A end root equals 2 space o r space A space equals negative 3 semicolon

B space equals space 80 plus A space equals space 80 minus 3 space equals space 77 semicolon end style
 
Hence the answer is A = -3 and B = 77;
 
Student should substitute these values of A and B in the given quadratic equations,
find the roots and verify the roots are in Arithmatic progression
Answered by Expert 14th December 2017, 5:12 PM
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