If roots of #x^2-4x+1# is #alpha# & #beta# then #alpha^beta*beta^alpha# is?

1 Answer
1s2s2p
Apr 25, 2018

#alpha^beta*beta^alpha~~0.01#

Explanation:

Roots are:
#x=(4+-sqrt((-4)^2-4))/2#

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

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

#x=(4+-2sqrt2)/2#

#x=2+sqrt3 or 2-sqrt3#

#alpha^beta*beta^alpha=(2+sqrt3)^(2-sqrt3)*(2-sqrt3)^(2+sqrt3)~~0.01#

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