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Each of the distinct numbers A and B exceeds its reciprocal by Unity. Find the value of a + b 
Asked by tusharbailwal8 | 24 Apr, 2019, 17:28: PM
answered-by-expert Expert Answer
space a space a n d space b space a r e space t w o space n u m b e r s space s u c h space t h a t space t h e y space e x c e e d space t h e i r space r e s p e c t i v e space r e c i p r o c a l s space b y space 1 rightwards double arrow a equals 1 plus 1 over a space a n d space b equals 1 plus 1 over b rightwards double arrow a equals fraction numerator a plus 1 over denominator a end fraction space a n d space b equals fraction numerator b plus 1 over denominator b end fraction rightwards double arrow a squared minus a minus 1 equals 0 space a n d space b squared minus b minus 1 equals 0 rightwards double arrow a equals fraction numerator 1 plus-or-minus square root of 1 plus 4 end root over denominator 2 end fraction space a n d space b equals fraction numerator 1 plus-or-minus square root of 1 plus 4 end root over denominator 2 end fraction rightwards double arrow a equals fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction space a n d space b equals fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction rightwards double arrow a plus b equals 2 open parentheses fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction close parentheses equals 1 plus-or-minus square root of 5 I f space a equals fraction numerator 1 plus square root of 5 over denominator 2 end fraction rightwards double arrow 1 plus 1 over a equals 1 plus fraction numerator 2 over denominator 1 plus square root of 5 end fraction space space space space space space space space space space space space space equals fraction numerator 3 plus square root of 5 over denominator 1 plus square root of 5 end fraction equals fraction numerator square root of 5 plus 3 over denominator square root of 5 plus 1 end fraction space space space space space space space space space space space space equals fraction numerator square root of 5 plus 3 over denominator square root of 5 plus 1 end fraction cross times fraction numerator square root of 5 minus 1 over denominator square root of 5 minus 1 end fraction space space space space space space space space space space space space space equals fraction numerator 5 minus square root of 5 plus 3 square root of 5 minus 3 over denominator 5 minus 1 end fraction space space space space space space space space space space space space equals fraction numerator 2 plus 2 square root of 5 over denominator 4 end fraction space space space space space space space space space space space space equals fraction numerator 1 plus square root of 5 over denominator 2 end fraction equals a S i m i l a r l y comma space w e space c a n space v e r i f y space f o r space a equals fraction numerator 1 minus square root of 5 over denominator 2 end fraction space a n d space f o r space b equals fraction numerator 1 plus-or-minus square root of 5 over denominator 2 end fraction H e n c e comma space a plus b equals 1 plus-or-minus square root of 5
Answered by Renu Varma | 25 Apr, 2019, 10:00: AM

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