Question #2b050

1 Answer
Manikandan S.
Jun 24, 2015

Square the both sides

Explanation:

#|x^2-3x|=-4x+6#
#sqrt((x^2-3x)^2)=-4x+6#
#x^2(x-3)^2=(-4x+6)^2#
#x^2(x^2-6x+9)=16x^2-48x+36#
#x^4-6x^3+9x^2-16x^2+48x-36=0#
#x^4-6x^3-7x^2+48x-36=0#
As sum of all coefficients are zero, x-1 is a factor.
#(x-1)(x^3-5x^2-12x+36)=0#
The rest of the cubic polynomial can be factored as #6*2*-3#
So the roots are now #x=1,2,6,-3#

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