Solve for x: 4(x-1/x)² + 8( x+1/x)=29

Asked by rajinderkaur1528 | 7th Mar, 2019, 02:10: PM

Expert Answer:

begin mathsize 12px style 4 open parentheses x minus 1 over x close parentheses squared space plus 8 open parentheses x plus 1 over x close parentheses space equals space 29
4 open square brackets open parentheses x plus 1 over x close parentheses squared space minus space 4 close square brackets space plus 8 open parentheses x plus 1 over x close parentheses space equals space 29
4 open parentheses x plus 1 over x close parentheses squared space plus 8 open parentheses x plus 1 over x close parentheses space minus space 45 space equals space 0
l e t space open parentheses x space plus space 1 over x close parentheses space equals space p space
w e space h a v e space comma space 4 p squared space plus space 8 p space minus 45 space equals space 0
b y space f a c t o r i sin g space L H S comma space open parentheses 2 p minus space 5 close parentheses space open parentheses 2 p plus 9 close parentheses space equals space 0 space space space.......... left parenthesis 1 right parenthesis

i f space p space equals space 5 divided by 2 comma space space t h e n space space x plus 1 over x space equals space 5 over 2 space space space o r space space space space space space space 2 x squared space minus 5 x space plus 2 space equals space space 0 space space
B y space f a c t o r i sin g space a b o v e space q u a d r a t i c space e q u a t i o n comma space space left parenthesis space x space minus space 2 right parenthesis space left parenthesis 2 x space minus space 1 space right parenthesis space space equals space 0
h e n c e space x space equals space 2 space space o r space space x space equals space 1 half
i f space space p space equals space minus 9 divided by 2 space comma space space t h e n space space x space plus space 1 over x space equals space minus 9 over 2 space space space o r space space space space space space space 2 x squared space plus 9 x space plus 2 space space equals space 0
h e n c e space space x space equals space fraction numerator negative 9 space plus-or-minus space square root of 81 space minus 16 end root over denominator 4 end fraction space space equals space fraction numerator negative 9 space plus-or-minus space square root of 65 over denominator 4 end fraction

end style

Answered by Thiyagarajan K | 7th Mar, 2019, 04:31: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.