ANSWER
D) 10
EXPLANATION
We want to solve the radical equation,
[tex] \sqrt{6n - 11} = n - 3[/tex]
Square both sides,
[tex]6n - 11 = (n - 3) ^{2} [/tex]
Expand brackets on right hand side,
[tex]6n - 11 = {n}^{2} - 6n + 9[/tex]
Rewrite in general quadratic equation form,
[tex] {n}^{2} - 12n + 20 = 0[/tex]
Factor to obtain,
[tex](n - 2)(n - 10) = 0[/tex]
Apply the zero product principle to get,
[tex]n = 2 \: or \: n = 10[/tex]
We put n=2 into the equation to get,
[tex] \sqrt{6(2) - 11} = 2 - 3[/tex]
[tex] 1 = - 1[/tex]
This statement is false, hence 2 is an extraneous solution
We put n=10, to get
[tex] \sqrt{6(10) - 11} = 10 - 3[/tex]
[tex] \sqrt{49} = 7[/tex]
[tex]7 = 7[/tex]
This is true, hence the only solution is
[tex]n = 10[/tex]
