If x = fraction numerator 1 over denominator square root of 5 minus 2 end fraction then value of x if
(i) x squared space plus space 1 over x squared
(ii)x squared space minus space 1 over x squared

Asked by vatsalchoudhary41 | 29th Jun, 2014, 11:11: AM

Expert Answer:

x equals fraction numerator 1 over denominator square root of 5 minus 2 end fraction T h e n 1 over x equals square root of 5 minus 2 rightwards double arrow x plus 1 over x equals fraction numerator 1 over denominator square root of 5 minus 2 end fraction plus square root of 5 minus 2 rightwards double arrow x plus 1 over x equals fraction numerator 1 plus open parentheses square root of 5 minus 2 close parentheses squared over denominator square root of 5 minus 2 end fraction rightwards double arrow x plus 1 over x equals fraction numerator 1 plus open parentheses 5 plus 4 minus 4 square root of 5 close parentheses over denominator square root of 5 minus 2 end fraction rightwards double arrow x plus 1 over x equals fraction numerator 10 minus 4 square root of 5 over denominator square root of 5 minus 2 end fraction rightwards double arrow x plus 1 over x equals fraction numerator 2 square root of 5 open parentheses square root of 5 minus 2 close parentheses over denominator square root of 5 minus 2 end fraction rightwards double arrow x plus 1 over x equals 2 square root of 5 rightwards double arrow open parentheses x plus 1 over x close parentheses squared equals 4 cross times 5 rightwards double arrow open parentheses x plus 1 over x close parentheses squared equals 20..... left parenthesis 1 right parenthesis N o w space c o n s i d e r comma space open parentheses x plus 1 over x close parentheses squared equals x squared plus 1 over x squared plus 2 rightwards double arrow x squared plus 1 over x squared equals space open parentheses x plus 1 over x close parentheses squared minus 2 rightwards double arrow x squared plus 1 over x squared equals 20 minus 2 space space space space space open square brackets f r o m space left parenthesis 1 right parenthesis close square brackets rightwards double arrow x squared plus 1 over x squared equals 18 space

(ii)

N o w space l e t space u s space f i n d space x minus 1 over x : x minus 1 over x equals fraction numerator 1 over denominator square root of 5 minus 2 end fraction minus open parentheses square root of 5 minus 2 close parentheses rightwards double arrow x minus 1 over x equals fraction numerator 1 minus open parentheses square root of 5 minus 2 close parentheses squared over denominator square root of 5 minus 2 end fraction rightwards double arrow x minus 1 over x equals fraction numerator 1 minus open parentheses 5 plus 4 minus 4 square root of 5 close parentheses over denominator square root of 5 minus 2 end fraction rightwards double arrow x minus 1 over x equals fraction numerator 1 minus 9 plus 4 square root of 5 over denominator square root of 5 minus 2 end fraction rightwards double arrow x minus 1 over x equals fraction numerator minus 8 plus 4 square root of 5 over denominator square root of 5 minus 2 end fraction rightwards double arrow x minus 1 over x equals fraction numerator 4 open parentheses square root of 5 minus 2 close parentheses over denominator square root of 5 minus 2 end fraction rightwards double arrow x minus 1 over x equals 4

W e space k n o w space t h a t space x squared minus 1 over x squared equals open parentheses x plus 1 over x close parentheses open parentheses x minus 1 over x close parentheses rightwards double arrow space x squared minus 1 over x squared equals 2 square root of 5 cross times 4 rightwards double arrow space x squared minus 1 over x squared equals 8 square root of 5

Answered by Vimala Ramamurthy | 30th Jun, 2014, 09:23: AM

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