How do you solve #t - sqrt (6t - 9) = 0#?

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Answer 1 · 2016-02-05T13:58:01

# t= 3#

Given: #t-sqrt(6t-9)=0#.......................(1)

Things would be easier if we 'got rid' of the square root!

#t=sqrt(6t-9)#

Square both sides

#t^2=6t-9#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Make into a quadratic equation

#t^2-6t+9=0#

Observe that#" " -3-3=-6 " and that " (-3)xx(-3)=+9#

Factorising gives:

#(t-3)^2=0#

so#" " t= +3#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check if correct!

Substituting for t in equation 1 and consider the left hand side only

#3-sqrt(6(3)-9)#

#3-sqrt(18-9)#

#3-(+-3)#

The only possible value for the LHS to be zero is to have:

#LHS->3-3=0" and " RHS->0# so proven to be correct