How do you solve #9x^2 = x^3 #?

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Answer 1 · 2016-05-18T04:51:04

#x=0#
#x=9#

Given -

#9x^2=x^3#
#9x^2-x^3=0#
#x^2(9-x)=0#
#x^2=0#
#x=0#
#9-x=0#
#x=9#

Answer 2 · 2016-05-19T03:06:30

#=> x = 0 or 9#

While most people would straightaway cancel the #x^2# on both sides .I would find that rather foolish.

This is an important concept to have not to cancel x terms on either side of the equation but to bring everything over to one side

#9x^2 = x^3#

#9x^2 -x^3 = 0#

#x^2(9 -x) = 0#

#=> x^2 = 0 or 9-x = 0#

#=> x = +-0 or x = 9#

So we get our 3 solutions out of which 2 are not distinct roots