Question

Solve the following radical equation. Enter your answer as an integer. If there is no solution indicate "No Solution" sqrt(5t - 11) = t - 1

Answer 1

ANSWER

$t=4,3$

EXPLANATION

Given;

$\sqrt{5t-11}=t-1$

Square both sides;

$\begin{gathered} \left(\sqrt{5t-11}\right)^2=\left(t-1\right)^2 \\ 5t-11=t^2-2t+1 \end{gathered}$

Solve and switch the sides;

$\begin{gathered} 5t-11=t^2-2t+1 \\ t^2-2t+1=5t-11 \end{gathered}$

Add 11 to both sides and simplify;

$\begin{gathered} t^2-2t+1+11=5t-11+11 \\ t^2-2t+12=5t \end{gathered}$

subtract 5t from both sides

$\begin{gathered} t^2-2t+12-5t=5t-5t \\ t^2-7t+12=0 \end{gathered}$

Solve the quadratic equation;

$\begin{gathered} t_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\cdot \:1\cdot \:12}}{2\cdot \:1} \\ t_1=\frac{-\left(-7\right)+1}{2\cdot \:1} \\ t_2=\frac{-\left(-7\right)-1}{2\cdot \:1} \\ t_1=\frac{8}{2}=4\frac{}{} \\ t_2=\frac{6}{2}=3 \\ \end{gathered}$

Therefore the solution to the quadratic equation are t=4, t=3