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

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