How do you solve #-2+ \sqrt { 5m - 1} = \sqrt { 1- m }#?

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Answer 1 · 2017-11-07T17:50:39

#m=1#

#-2+sqrt(5m-1)=sqrt(1-m)#

After squaring both sides,

#5m-1-4sqrt(5m-1)+4=1-m#

#6m+2=4sqrt(5m-1)#

#3m+1=2sqrt(5m-1)#

After squaring both sides again,

#(3m+1)^2=4*(5m-1)#

#9m^2+6m+1=20m-4#

#9m^2-14m+5=0#

#9m^2-9m-5m+5=0#

#9m*(m-1)-5*(m-1)=0#

#(9m-5)*(m-1)=0#

#m=5/9# doesn't provide a solution. Hence #m=1#