Prove the following ?

Question

#x+1/x=4#
#x=sqrt(7+sqrt3)#

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Answer 1 · 2018-06-25T04:29:26

#x=2+-sqrt3#

#x+1/x=4# where #x !=0#

#x^2+1=4x#

#x^2-4x+1=0#

#x=(-b+-sqrt(b^2-4ac))/(2a)#

#x=(4+-sqrt(16-4))/2#

#x=(4+-sqrt12)/2#

#x=(4+-2sqrt3)/2#

#x=2+-sqrt3#

Answer 2 · 2018-06-25T05:16:34

Given

#x+1/x=4.....(1)# where #x !=0#

#(x-1/x)^2=(x+1/x)^2-4*x*1/x#

#=>(x-1/x)^2=4^2-4=12#

#=>x-1/x=pm2sqrt3....(2)#

Adding (1) and (2)

#2x=4pm2sqrt3#

#=>x=2pmsqrt3#